Identification of an accurate and simple model of a complex underactuated crane dynamics for varying operational conditions is a crucial step towards designing and implementation of real-time monitoring and control systems to enhance crane safety and operational efficiency. This paper considers a non-parametric data-driven identification of an overhead crane dynamics using symbolic regression techniques to find compromise between model complexity and predicted output accuracy. A grammar-guided genetic programming (G3P) combined with l0 sparse regression is applied with two different variants of grammar to automatically construct a nonlinear autoregressive exogenous (NARX) model of different forms, termed extended and polynomial models. The proposed method is compared with a linear parameter-varying ARX (LPV-ARX) model. Identification is performed on experimental data obtained from a laboratory-scale overhead crane. The identified models are compared in terms of prediction accuracy, model’s complexity measured using number of model terms, and execution time. The regularized G3P method outperformed the LPV-ARX model in terms of model predictive output accuracy. The G3P with the extended grammar resulted in more accurate crane velocity prediction models than the models with the polynomial grammar. The payload sway prediction model with the polynomial grammar was less complex in all measured metrics while there was no statistical significance in the accuracy when compared to the models with extended grammar.