Index tracking is a form of passive portfolio management, which mimics a target index performance and expects to achieve similar returns as close as possible. In this paper, first we review, implement and compare the performance of several index tracking models by using the data of HengSeng Index and its fifty components. The models considered in this thesis are the Cointegration, Capital Assets Pricing Model, Fama and French three factors model, and Principle Components Analysis. Within the data sample, CAPM get the better performance among the model we implement. Second, due to the highly nonlinear issue in the index tracking problem, we implement the Genetic Algorithm (GA) in the optimization procedure and show that a generally better tracking performance, in terms of minimizing tracking error, is achieved. GA is a search routine that mimics the natural selection, and belongs to a large family called evolutionary algorithms. To the best of our knowledge, this is the first article to study the performance of the combination the GA with the standard index tracking models used in financial literature. Tracking portfolio performance is presented by three popular tracking error measurements, tracking error variance (TEV), mean error (ME), and mean absolute deviation (MAD). In regard to model CAPM and Fama French three factors model, in additional we illustrate the trade-off between tracking error and the transaction cost for each tracking portfolio with different portfolio size (numbers of candidates in the tracking portfolio), and then we figure out the proper range of portfolio size.