Because of the multi-colinearity of the ill-conditioned mixing signals, it is difficult to solve the issue of underdetermined blind sources separation for ill-conditioned mixing signals in noisy environment by Sparse Component Analysis (SCA). The model of the problem is built and the limitation of clustering methods to solve the problem is analyzed in this paper. Then a robust underdetermined blind sources separation algorithm based on SCA and Nonorthogonal Joint Diagonalization (NJD) is presented. NJD has the property that the mixing matrix is not necessarily unitary, which is used to solve the above problem in the novel algorithm. Simulation experiments show that the algorithm can improve the performance in separation performance, noise robust and ill-conditioned mixing robust compared with Cluster Guide Particle Swarm Optimization (CGPSO) algorithm.