The Marchenko method is a data-driven way which makes it possible to calculate Green's functions from virtual points in the subsurface by the reflection data at the surface, only requiring a macro velocity model. This method requires collocated sources and receivers. However, in practice, subsampling of sources or receivers will cause gaps and distortions in the obtained focusing functions and Green's functions. To solve this problem, this paper proposes to integrate sparse inversion into the iterative Marchenko scheme. Specifically, we add sparsity constraints to the Marchenko equations and apply sparse inversion during the iterative process. Our work not only reduces the strict requirements on acquisition geometries, but also avoids the complexity and instability of direct inversion for Marchenko equations. This new method is applied to a two-dimensional numerical example with irregular sampled data. The result shows that it can effectively fill gaps of the obtained focusing functions and Green's functions in the Marchenko method.