Based on the results of the global existence of weak solutions of three-dimensional chemotaxis system, this paper further considers the final smoothness of the weak solutions of a class of parabolic chemotaxis equations with logistic source under the corresponding homogeneous Neumann initial boundary value conditions in three-dimensional case. In this paper, the higher-order regularity estimation of the solution is obtained by constructing the energy functional and using Sobolev maximum regularity theory, Sobolev embedding theorem, Gagliardo Nirenberg inequality, Young inequality, H?lder inequality, Poincaré inequality, compact embedding theorem and Gronwall inequality. The results show that for any nonnegative and appropriate initial value, it can be proved that the weak solution of the system becomes a classical solution after a certain waiting time.