In order to solve the problems of poor real-time performance, significant tracking errors and poor robustness to clutter changes with maneuvering multi-target tracking with nonlinear measurement, a multi-model δ-generalized labeled multi-Bernoulli (δ-GLMB) filter is proposed in light of the random finite set (RFS) theory, capitalizing on measurement transformation and a fuzzy algorithm. Initially, the interactive multiple model (IMM) δ-GLMB filter realizes the unbiased conversion of position measurement from polar coordinate system to Cartesian coordinate system by initiating an uncorrelated unbiased measurement conversion and removes the filter estimation deviation caused by the correlation between measurement errors and their covariances on the basis of the predicted value, thus realizing the maneuvering multi-target tracking in nonlinear scenarios. Then, the number of clutter measurements is reduced by constructing a joint gate that takes into account track and measurement correlation and target maneuver constraints. Finally, an improved fuzzy algorithm is introduced, which takes the posterior model probability of the target as the input, to adaptively adjust the process noise of the motion model according to the separation degree of the model, thereby increasing filtering accuracy. The research result shows that in the clutter environment, compared with CKF-JMS-δ-GLMB, CKF-IMM-δ-GLMB, and other nonlinear filters, the proposed algorithm performs better in terms of computation time, tracking accuracy and robustness. The proposed algorithm sidesteps the computational burden typically associated with traditional nonlinear processing methods, and has better clutter suppression characteristics, which improves the performance of maneuvering multi-target tracking with nonlinear measurement.