As a multi-task meta learning algorithm， Model Agnostic Meta Learning （MAML） can use different models and adapt quickly to different tasks， but it still needs to be improved in terms of training speed and accuracy. The principle of MAML was analyzed from the perspective of Gaussian stochastic process， and a new Model Agnostic Meta Learning algorithm based on Bayesian Weight function （BW-MAML） was proposed， in which the weight was assigned by Bayesian analysis. In the training process of BW-MAML， each sampling task was regarded as following a Gaussian distribution， and the importance of the task was determined according to the probability of the task in the distribution， and then the weight was assigned according to the importance， thus improving the utilization of information in each gradient descent. The small sample image learning experimental results on Omniglot and Mini-ImageNet datasets show that by adding Bayesian weight function， for training effect of BW-MAML after 2500 step with 6 tasks， the accuracy of BW-MAML is at most 1.9 percentage points higher than that of MAML， and the final accuracy is 0.907 percentage points higher than that of MAML on Mini-ImageNet averagely； the accuracy of BW-MAML on Omniglot is also improved by up to 0.199 percentage points averagely.