Temporal graph is a type of graph where each edge is associated with a timestamp. Seasonal-bursting subgraph is a dense subgraph characterized by burstiness over multiple time periods, which can applied for activity discovery and group relationship analysis in social networks. Unfortunately, most previous studies for subgraph mining in temporal networks ignore the seasonal or bursting features of subgraphs. To this end, this study proposes a maximal ($\omega,\theta $)-dense subgraph model to represent a seasonal-bursting subgraph in temporal networks. Specially, the maximal ($\omega,\theta $)-dense subgraph is a subgraph that accumulates its density at the fastest speed during at least $ \omega $ particular periods of length no less than $ \theta $ on the temporal graph. To compute all seasonal bursting subgraphs efficiently, the study first models the mining problem as a mixed integer programming problem, which consists of finding the densest subgraph and the maximum burstiness segment. Then corresponding solutions are given for each subproblem, respectively. The study further conceives two optimization strategies by exploiting key-core and dynamic programming algorithms to boost performance. The results of experiments show that the proposed model is indeed able to identify many seasonal-bursting subgraphs. The efficiency, scalability, and effectiveness of the proposed algorithms are also verified on five real-life datasets.