In general, one often encounters the systems that have sparse impulse response, with time varying system sparsity. Conventional adaptive filters which perform well for identification of non-sparse systems fail to exploit the system sparsity for improving the performance as the sparsity level increases. This paper presents a new approach that uses an adaptive convex combination of Affine Projection Algorithm (APA) and Zero-attracting Affine Projection Algorithm (ZA-APA)algorithms for identifying the sparse systems, which adapts dynamically to the sparsity of the system. Thus works well in both sparse and non-sparse environments and also the usage of affine projection makes it robust against colored input. It is shown that, for non-sparse systems, the proposed combination always converges to the APA algorithm, while for semi-sparse systems, it converges to a solution that produces lesser steady state EMSE than produced by either of the component filters. For highly sparse systems, depending on the value of the proportionality constant ($ρ$) in ZA-APA algorithm, the proposed combined filter may either converge to the ZA-APA based filter or produce a solution similar to the semi-sparse case i.e., outerperforms both the constituent filters.