A light scalar X-0 or vector X-1 particles have been introduced as a possible explanation for the (g - 2)(mu) anomaly and dark matter phenomena. Using (8.998 +/- 0.039) x 10(9) J=psi events collected by the BESIII detector, we search for a light muon philic scalar X-0 or vector X-1 in the processes J=psi -> mu(+)mu X--(0,1) with X-0,X-1 invisible decays. No obvious signal is found, and the upper limits on the coupling g'(0,1) between the muon and the X-0,X-1 particles are set to be between 1.1 x 10(-3) and 1.0 x 10(-2) for the X-0,X-1 mass in the range of 1 < M(X-0,X-1) < 1000 MeV=c(2) at 90% credibility level.