A hybrid uncertain parameter model (HUPM) is introduced to predict the luffing angular response (LAR) field of the dual automobile cranes system (DACS) with random and interval parameters. In the model, all random parameters with specified probabilistic distributions comprise a random vector, while all interval parameters with determined bounds comprise an interval vector. A hybrid uncertain LAR equilibrium equation is established, and a novel approach named as hybrid perturbation compound function-based moment method is proposed based on the HUPM. In the hybrid perturbation compound function-based moment method, the expression of LAR is developed according to the random interval perturbation compound function-based method. More, by using the random interval compound function-based moment method and the monotonic technique, the expectations and variances of the bounds for LAR are calculated. Compared with the hybrid Monte Carlo method (HMCM) and interval perturbation method (IPM), numerical results on different uncertain cases of the DACS demonstrate the feasibility and efficiency of the proposed algorithm. The proposed method is proved to be an effective engineering method to quantify the effects of hybrid uncertain parameters on the LAR of DACS.