The massive non-Abelian gauge fields are quantized Lorentz-covariantly in the
Hamiltonian path-integral formalism. In the quantization, the Lorentz
condition, as a necessary constraint, is introduced initially and incorporated
into the massive Yang-Mills Lagrangian by the Lagrange multiplier method so as
to make each temporal component of a vector potential to have a canonically
conjugate counterpart. The result of this quantization is confirmed by the
quantization performed in the Lagrangian path-integral formalism by applying
the Lagrange multiplier method which is shown to be equivalent to the
Faddeev-Popov approach.