This letter presents a robust solution for joint sparse recovery (JSR) under impulsive noise. The unknown measurement noise is endowed with the Student-t distribution, then a novel Bayesian probabilistic model is proposed to describe the JSR problem. To effectively recover the joint row sparse signal, variational Bayes (VB) method is introduced for Bayesian theory based JSR algorithms such that it overcomes the intractable integrations inherent. Simulation results verify that the proposed algorithm significantly outperforms the existing algorithms under impulsive noise.