Received signal strength (RSS) measurement based source localization is highly dependent on the propagation model. However, such propagation model is not easy to be captured in the practical applications. In this paper, we address the multiple sources localization (MSL) problem while jointly estimating parametric propagation model. Specifically, we model the localization problem as being parameterized by the unknown source locations and propagation parameters. Then, the localization problem is reformulated as a joint parametric sparsifying dictionary learning (PSDL) and sparse signal recovery (SSR) problem. Finally, the problem is solved under the framework of sparse Bayesian learning with parametric dictionary approximation. We compare the proposed method with the state-of-the-art MSL algorithms as well as Cramér-Rao lower bound (CRLB). Numerical simulations highlight the effectiveness of the proposed method.