Image super-resolution (SR) reconstruction has been a hot research topic in recent years. This technique allows the recovery of a high-resolution (HR) image from several low-resolution (LR) images that are noisy, blurred and down-sampled. Among the available reconstruction frameworks, the maximum a posteriori (MAP) model is widely used. In this model, the regularization parameter plays an important role. If the parameter is too small, the noise will not be effectively restrained; conversely, the reconstruction result will become blurry. Therefore, how to adaptively select the optimal regularization parameter has been widely discussed. In this paper, we propose an adaptive MAP reconstruction method based upon a U-curve. To determine the regularization parameter, a U-curve function is first constructed using the data fidelity term and prior term, and then the left maximum curvature point of the curve is regarded as the optimal parameter. The proposed algorithm is tested on both simulated and actual data. Experimental results show the effectiveness and robustness of this method, both in its visual effects and in quantitative terms.