In view of the lack of effective resource demand forecasting and optimal allocation in Platform-as-a-Service (PaaS) platform, a resource demand forecasting model and an allocation method were proposed. Firstly, according to the periodicity of the application demand for resources in PaaS platform, the resource sequence was segmented. And on the basis of short-term prediction, combined with the multi-periodicity characteristics of the application, a comprehensive prediction model was established by using the multiple regression algorithm. Then, based on MapReduce architecture, a PaaS platform resource allocation system based on Master-Slave mode was designed and implemented. Finally, the resources were allocated based on current task request and resource demand prediction results. The experimental results show that, compared with autoregressive model and exponential smoothing algorithm, the proposed resource demand forecasting model and allocation method has the mean absolute percentage error drop of 8.71 percentage points and 2.07 percentage points respectively, root mean square error drop of 2.01 percentage points and 0.46 percentage points respectively. It can be seen that the prediction result of the prediction model has little error and its fitting degree with real value is high, while high accuracy costs little time. Besides, the average waiting time of PaaS platform with the proposed prediction model for resource requests decreases significantly.