Aiming at the problem of data sparsity caused by few connections between users and service nodes in World Wide Web （Web） Quality of Service （QoS） prediction， as well as the cold start problem caused by the lack of historical call data， a QoS prediction model for data sparsity and cold start problems was proposed. Firstly， a random propagation strategy was adopted， where multiple augmented graphs were generated by dropping nodes randomly for propagation， so as to achieve data augmentation. At the same time a consistency regularization method was used to optimize the prediction consistency between multiple augmentations， thereby alleviating the data sparsity. Secondly， a multi-factor similarity calculation method was proposed， so that random node dropping was combined to construct user and service context subgraphs. Thirdly， graph contrastive learning was introduced to train each subgraph， making the context embedding representations of similar nodes closer， thereby alleviating the cold start. Experimental results show that compared with the existing QoS prediction models， this model maintains better performance in all scenarios with data density from 0.5% to 4.0%. It can be seen that this model provides a new paradigm for graph random neural network to process sparse data theoretically， and in application， it can improve the service recommendation accuracy of platforms such as community intelligent management and e-commerce， as well as reduce the trial-and-error cost of service calls.