The nonsynchronous measurements of microphone array are a powerful method for achieving large array or high microphone density by scanning the object from a sequential movement of a prototype array. It has attracted great interest recently because it is beyond the fundamental limitation of working frequency that is determined by the aperture and microphone density of an array. A crucial problem of nonsynchronous measurements is to recover the missing phase relation information between consecutive positions. The problem in traditional solution is generally attributed to the matrix completion problem of a block diagonal spectral matrix. In this paper, the issue has been investigated as a problem of solving a system of equations in the Bayesian formalism. The intrusive Gibbs sampling method is proposed to reconstruct the source in the equations. In the numerical simulations, convergence diagnosis of the Markov chain is illustrated through three approaches. Acoustical source reconstruction error is also discussed with respect to the frequency range, signal-to-noise ratio, measurement distances, and shift distance of sequential movement. The proposed method is exhibited to return similar results with the expectation maximization algorithm of nonsynchronous measurements. The effectiveness of the proposed method is also validated by experiments in a semi-anechoic chamber.