Considering that the spatial relationship between channels affects the noise reduction， graph signal processing can capture the potential relationship. If the spatial physical distribution map is directly used， its time-varying characteristics cannot be reflected in real time. Therefore， we propose a multi-channel speech enhancement method based on joint graph learning. Firstly， we propose a joint time-space graph learning method， which jointly optimizes the array space graph and the speech frame inner graph， for the sake of minimizing the sum of the smoothness of the multi-channel noisy speech signal on the spatial graph， the smoothness of the nosiy speech signal from the reference channel on the speech frame graph， the sparsity of the Laplace matrix and the sparsity of the adjacency matrix. Based on the learned space graph and frame inner graph， the time-space joint graph of multi-channel speech signal is constructed. On this basis， the multi-channel speech graph signal is enhanced by applying the joint graph transform and the fixed beam forming （FBF） method. Experimental results show that the proposed joint graph learning based FBF （JGL-FBF） method can significantly improve the signal-to-noise ratio （SNR） of enhanced speech and perceptual evaluation of speech quality （PESQ） compared with the traditional FBF method. In addition， the experimental results also show that the accuracy of delay compensation affects the speech enhancement performance of JGL-FBF.