Massive multiple-input multiple-output (MIMO) is a key technique in the fifth-generation (5G) networks for its attractive advantages in wireless communication. Besides, it also provides localization capability with high accuracy, yet the massive MIMO localization problem is not well addressed with the presence of some physical impairments in the circuits, such as phase noise (PHN). In this paper, we consider localization problem with PHN, which is a critical bottleneck in massive MIMO. Traditionally, existing methods exploit channel sparsity by sampling the space into discrete grids to estimate the position of the user in the compressive sensing framework. However, as the PHN affects the received signal in a nonlinear manner, it is difficult to obtain accurate basis vectors for sparse channel recovery. Besides, they often suffer from performance loss due to the location quantization error introduced by the fixed location grid. To deal with the aforementioned problems, we introduced a sparse representation model for the channel with dynamic-grid parameters to eliminate the location quantization error and derived an approximation for the likelihood with the presence of PHN. Based on these, we proposed an efficient algorithm for joint estimation of user location and sparse channel utilizing the majorization-minimization algorithm, which is shown to achieve higher localization accuracy than existing methods with the presence of PHN.