The stochastic nature of renewable energy sources has increased the need for intraday trading in electricity markets. Intraday markets provide the possibility to the market participants to modify their market positions based on their updated forecasts. In this paper, we propose a multistage stochastic programming approach to model the trading of a Virtual Power Plant (VPP), comprising thermal, wind and hydro power plants, in the Continuous Intraday (CID) electricity market. The order clearing in the CID market is enabled by the two presented models, namely the Immediate Order Clearing (IOC) and the Partial Order Clearing (POC). We tackle the proposed problem with a modified version of Stochastic Dual Dynamic Programming (SDDP) algorithm. The functionality of our model is demonstrated by performing illustrative and large scale case studies and comparing the performance with a benchmark model.