A potential with three parameters is used in a light-cone equation for a quark-antiquark pair. Spin dependence is not included. The nonrelativistic limit is the potential of the quark model of Eichten et al. Numerical methods are used to solve the eigenvalue problem. The parameters and quark masses are varied to obtain a reasonable fit to masses of low-lying hidden-flavor mesons. Additional masses are calculated for higher states and for flavored mesons. Also, properties of the pion are calculated from a wave function obtained with the numerical method. Spectroscopic assignments are problematic because the light-front formulation breaks rotational invariance. A need for an improved treatment of angular momentum eigenstates is indicated.