In this paper, we consider the phase recovery problem, where a complex signal vector has to be estimated from the knowledge of the modulus of its linear projections, from a naive variational Bayesian point of view. In particular, we derive an iterative algorithm following the minimization of the Kullback-Leibler divergence under the mean-field assumption, and show on synthetic data with random projections that this approach leads to an efficient and robust procedure, with a good computational cost.