This article examines the problems of model correction and parameter estimation in sparse representation for passive radar sensing. The on-grid assumption brings implementation convenience to sparse representations but leads to model mismatch and parameter discretization errors. To address these problems, we propose a sparse representation method that can adaptively correct the model mismatch and does not depend on the special structure of the signal waveform. First, we initialize the 2-D delay-Doppler grid using uniform interval parameters. Then, an alternating linear approximation strategy in the time and frequency domains is used to estimate and compensate for the Doppler and delay grid deviations, respectively. After several iterations, the atoms are moved to overlap with each signal component, thus reducing the model mismatch and improving the parameter estimation accuracy. Both simulation and field experimental results under the scenario of FM radio-based passive radar verify the effectiveness of the proposed algorithm.