Multi-project management and uncertain environment are very common factors, and they bring greater challenges to scheduling due to the increase of problem complexity and response efficiency requirements. In this paper, a novel hyper-heuristic based filtering genetic programming (HH-FGP) framework is proposed for evolving priority rules (PRs) to deal with a multi-project scheduling problem considering stochastic activity duration and new project insertion together, namely the Stochastic Resource Constrained Multi-Project Scheduling Problem under New Project Insertions (SRCMPSP-NPI), within heuristic computation time. HH-FGP is designed to divide traditional evolution into sampling and filtering evolution for simultaneously filtering two kinds of parameters constituting PRs, namely depth range and attribute, to obtain more effective PRs. Based on this, the existing genetic search and local search are improved to meet the depth constraints, and a multi-objective evaluation mechanism is designed to achieve effective filtering. Under the existing benchmark, HH-FGP is compared and analysed with the existing methods to verify its effectiveness.