Fractional differential equations, which involve a fractional-order derivative in time or/and space, have attracted great interest in recent years. Their practical applications is very broad and span many diverse disciplines, e.g., subsurface flow, thermal diffusion in fractal domains, and dynamics of protein molecules. It is well-known that closed-form analytic solutions of fractional differential equations are usually not available especially when the equations are nonlinear. Therefore, studying reliable numerical schemes for the fractional differential equations becomes an urgent topic. In this thesis, we study linearized finite difference schemes for solving three types of time-fractional nonlinear equations: time-fractional Klein-Gordon type equations, time-fractional Burgers type equations, and time-fractional Benjamin-Bona-Mahony (BBM) type equations. The advantage of the linearized method is that iterative method is not required for finding the approximated solutions, which will simplify the theoretical analysis and save computations for our considered problems. The concept of fractional derivative, and some backgrounds of fractional differential equations and finite difference method will be introduced in the first Chapter. In Chapter 2, by applying a weighted approach, we derive a second-order weighted approximation (base on the L2-1σ,formula) to Caputo fractional derivative of order1 < α < 2. Meanwhile, we construct a fitted second-order approximation which will be used for approximating the grid function on diffusion term of Klein-Gordon type and Burgers type equations, its structure is important to the analysis of our linearized schemes. Some lemmas, which are necessary for theoretical analysis, are also presented. In Chapter 3, based on the second-order weighted approximation introduced in Chapter 2,we propose a linearized finite difference scheme for solving the time fractional Klein-Gordon type equations. By making use of the properties discussed in Chapter 2, and careful estimating the bound of each product terms, we show that the proposed scheme is second-order convergent in time and space. To improve the spatial accuracy, we further construct a compact scheme which converges with fourth-order in space. Some numerical examples are given to justify the accuracy. Comparisons (theoretical and numerical) between the second-order linearized scheme with some other schemes are also included to show the advantages of our proposed method. In Chapter 4, also based on the second-order weighted approximation derived in Chapter 2,we propose a linearized finite difference scheme for solving the time-fractional Burgers type equations. The nonlinear term of the problem involves derivatives causes difficulties in analysis. By refining estimates of those for Klein-Gordon type equations, we show that the scheme is second-order unconditionally convergent in maximum-norm. Numerical results are presented to verify the theoretical statements. In Chapter 5, we consider the BBM type equation with a fractional order derivative 0 < γ < 1 in time. By applying a different weighted approach to that in Chapter 2 and also based on the L2-1σ, we construct a linearized finite difference scheme to solve the nonlinear problem. With some similar techniques which were applied in the analysis of Klein-Gordon type and Burgers type problems, we show that the proposed scheme is unconditionally convergent with second-order in time and space within maximum-norm estimate. Numerical examples are included to confirm the efficiency. Finally, we give a concluding remark and briefly discuss some future research in Chapter 6.