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In this paper,the period-adding route to complex coexistence is analyzed by using the numerical simulations in an inertial neuron system with two time delays.The system exhibited the stability coexistences of two ASP-3 (anti-symmetric periodical solution with period 3),one SSP-1 (self-symmetric periodical solution with period 1),and one SSP-3 solutions (self-symmetric periodical solution with period 3) employing the period-adding route and pitchfork bifurcation of periodic solution.Further,the increasing delay gives rise to the coexistence of several multi-periodical and quasi-periodical solutions.