Focusing on the issue that the Least Absolute Shrinkage and Selection Operator (LASSO) algorithm may introduce some false targets in moving target detection with the presence of multipath reflections, a descending dimension method for designed matrix based on LASSO was proposed. Firstly, the multipath propagation increases the spatial diversity and provides different Doppler shifts over different paths. In addition, the application of broadband OFDM signal provides frequency diversity. The introduction of spatial diversity and frequency diversity to the system causes target space sparseness. Sparseness of multiple paths and environment knowledge were applied to estimate paths along the receiving target responses. Simulation results show that the improved LASSO algorithm based on the descending dimension method for designed matrix has better detection performance than the traditional algorithms such as Basis Pursuit (BP), Dantzig Selector (DS) and LASSO at the Signal-to-Noise Ratio (SNR) of -5 dB, and the target detection probability of the improved LASSO algorithm was 30% higher than that of LASSO at the false alarm rate of 0.1. The proposed algorithm can effectively filter the false targets and improve the radar target detection probability.