In the last decade, several algorithms have been proposed for performance improvement of adaptive filters in sparse system identification. In this paper, we propose a new convex combination of two different algorithms as zero-attracting leaky least-mean-square (ZA-LLMS) and reweighted zero-attracting leaky-least-mean square (RZA-LLMS) algorithms in sparse system identification setting. The performances of the aforementioned algorithms has been tested and compared to the result of the new combination. Simulations show that the proposed algorithm has a good ability to track the MSD curves of the other algorithms in additive white Gaussian noise (AWGN) and additive correlated Gaussian noise (ACGN) environments.