Due to the short wavelength of millimeter-wave, active electrical scanning millimeter-wave imaging system requires large imaging scenarios and high resolutions in practical applications. These requirements lead to a large uniform array size and high complexity of the feed network that satisfies the Nyquist sampling theorem. Accordingly, the system faces contradictions among imaging accuracy, imaging speed, and system cost. To this end, a novel, Credible Bayesian Inference of near-field Sparse Array Synthesis (CBI-SAS) algorithm is proposed under the framework of sparse Bayesian learning. The algorithm optimizes the complex-valued excitation weights based on Bayesian inference in a sparse manner. Therefore, it obtains the full statistical posterior Probability Density Function (PDF) of these weights. This enables the algorithm to utilize higher-order statistical information to obtain the optimal values, confidence intervals, and confidence levels of the excitation weights. In Bayesian inference, to achieve a small number of array elements to synthesize the desired beam orientation pattern, a heavy-tailed Laplace sparse prior is introduced to the excitation weights. However, considering that the prior probability model is not conjugated with the reference pattern data probability, the prior model is encoded in a hierarchical Bayesian manner so that the full posterior distribution can be represented in closed-form solutions. To avoid the high-dimensional integral in the full posterior distribution, a variational Bayesian expectation maximization method is employed to calculate the posterior PDF of the excitation weights, enabling reliable Bayesian inference. Simulation results show that compared with conventional sparse array synthesis algorithms, the proposed algorithm achieves lower element sparsity, a smaller normalized mean square error, and higher accuracy for matching the desired directional pattern. In addition, based on the measured raw data from near-field 1D electrical scanning and 2D plane electrical scanning, an improved 3D time domain algorithm is applied for 3D image reconstruction. Results verify that the proposed CBI-SAS algorithm can guarantee imaging results and reduce the complexity of the system.