To solve the problem of multi-target tracking with heavy-tailed process noise and measurement noise, a Student's t mixture δ-generalized labeled multi-Bernoulli ( δ-GLMB) filter is proposed for nonlinear systems. A third-degree Spherical-Radial rule is utilized to calculate the probability density functions of the prediction and update of target states for nonlinear multi-target models. The performance of the proposed Student's t mixture δ-GLMB filter for nonlinear systems is compared with the Sequential Monte Carlo δ-GLMB (SMC- δ-GLMB) filter through simulation experiments. Simulation results demonstrated that the proposed filter can achieve a good trade-off between efficiency and tracking accuracy.