In this article,we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model,which describes the interaction between populations of prey and predator,and takes into account the economic interest.We firstly obtain the solvability condition and the stability of the model system,and discuss the singularity induced bifurcation phenomenon.Next,we introduce a state feedback controller to eliminate the singularity induced bifurcation phenomenon,and discuss the optimal control problems.Finally,numerical solutions and their simulations are considered in order to illustrate the theoretical results and reveal the more complex dynamical behavior.