We develop a nonlinear red tide dynamic model to study the effect on a system of two harmful phytoplankton and zooplankton and of a toxicant emitted into the environment from external sources and a toxin excreted by phytoplankton. We use modern nonlinear dynamics to discuss stability and bifurcation, and obtain the thresholds of persistence and extinction for each species. Numerical simulations are used to validate the theoretical results. The results show that a sequence of Hopf bifurcations occur at the interior equilibrium as the delay increases or the growth rates increase.