The aim of index-tracking approaches in portfolio optimization is to create a mimicking portfolio which tracks a specific market index. However, without regularization, this mimicking behavior of the index-tracking model is susceptible to the volatility in the market index and has negative effects on the tracking portfolio. We recast the index-tracking optimization problem by applying a form of regularization using the convex combination of 1 and squared 2 norm constraints on the portfolio weights. The proposed optimization model enables us to control the tracking performance and the sparsity structure of the portfolio simultaneously. A sample of assets from Borsa Istanbul (BIST) is used to demonstrate the performance of the regularized portfolios with various levels of regularization. Results indicated that the regularized portfolios obtained using this approach had better tracking performances with a desired sparsity structure compared to the standard index-tracking portfolio where no regularization is applied.