In this paper, the line spectral estimation (LSE) problem with multiple measurement vectors (MMVs) is studied utilizing the Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) method, we develop the multisnapshot VALSE (MVALSE) for multi snapshot scenarios, which is especially important in array signal processing. The MVALSE shares the advantages of the VALSE method, such as automatically estimating the model order, noise variance, weight variance, and providing the uncertain degrees of the frequency estimates. It is shown that the MVALSE can be viewed as applying the VALSE with single measurement vector (SMV) to each snapshot, and combining the intermediate data appropriately. Furthermore, the Seq-MVALSE is developed to perform sequential estimation. Finally, numerical results are conducted to demonstrate the effectiveness of the MVALSE method, compared to the state-of-the-art methods in the MMVs setting.