An identification method based on functional data analysis (FDA) and extreme learning machine (ELM) is presented to identify the contact parameters of a cannon cradle and its bushing. A virtual prototype of the cannon is built in ADAMS. The response curves of muzzle vertical acceleration with different contact parameters of the cradle and its bushing are obtained by simulation experiments and used for FDA as sample data. Features of the sample data are extracted by FDA and functional principle component analysis (FPCA), and the features and contact parameters are used to train the ELM. Simulation data and test data are used to verify the proposed method. The presented method is also proved to be feasible and effective by comparing actual muzzle vertical acceleration curve and the muzzle vertical acceleration curve from the virtual prototype with respect to the test data identification results.