Abstract The forward kinematics of parallel robots is a challenging issue due to its highly coupled non‐linear relation among branch chains. This paper presents a novel approach to forward kinematics of parallel robots based on kernel extreme learning machine (KELM). To tackle with the forward kinematics solution of fully parallel robots, the forward kinematics solution of parallel robots is equivalently transformed into a machine learning model first. On this basis, a computational model combining sparrow search algorithm and KELM is then established, which can serve as both regression and classification. Based on SSA‐optimised KELM (SSA‐KELM) established in this study, a binary discriminator for judging the existence of the forward kinematics solution and a multi‐label regression model for predicting the forward kinematics solution are built to obtain the forward kinematics general solution of parallel robots with different structural configurations and parameters. To evaluate the proposed model, a numerical case on this dataset collected by the inverse kinematics model of a typical 6‐DOF parallel robot is conducted, followed by the results manifesting that the binary discriminator with the discriminant accuracy of 88.50% is superior over ELM, KELM, support vector machine and logistic regression. The multi‐label regression model, with the root mean squared error of 0.06 mm for the position and 0.15° for the orientation, outperforms the double‐hidden‐layer back propagation (2‐BP), ELM, KELM and genetic algorithm‐optimised KELM. Furthermore, numerical cases of parallel robots with different structural configurations and parameters are compared with state‐of‐the‐art models. Moreover, these results of numerical simulation and experiment on the host computer demonstrate that the proposed model displays its high precision, high robustness and rapid convergence, which provides a candidate for the forward kinematics of parallel robots.