Because the test power of the traditional panel unit root tests is unstable and the choice of the null hypothesis of traditional panel unit root tests is subjective, this paper proposed a Bayesian quantile unit root test for panel data based on asymmetric Laplace distribution. On the basis of quantile autoregression panel data model, the full conditional distributions of parameters were inferred and MCMC algorithm was designed. And then, Bayesian quantile unit root tests were conducted. Numerical results were produced via a combination of Monte Carlo simulation, from which we find that Bayesian quantile unit root tests are noticeably efficient and feasible. As a result, it is shown that Bayesian quantile unit root tests solve unstable power problems and the subjective choice of the null hypothesis. Furthermore, the tests are more robust and can provide more complete information.