Quantitative T1ρ mapping typically requires the acquisition of multiple images with different spin-lock times, which greatly prolongs the scanning time, limiting its clinical applications. We developed a novel reconstruction method using a low-rank plus sparse model to obtain the parameter-weighted images from highly undersampled k-space data. This method exploited both the parameter-weighted image properties and priori information from the parameter model. Specifically, a signal compensation strategy was introduced to promote the low rankness along the parametric direction. The proposed method achieved a five-fold acceleration in the acquisition time and obtained more accurate T1ρ maps than the existing methods.