We study the decay constants (fM) of the heavy vector (D∗, Ds∗, B∗, Bs∗, Bc∗) and tensor (D2∗, Ds2∗, B2∗, Bs2∗) mesons in the light front quark model. With the known pseudoscalar meson decay constants of fD, fDs, fB, fBs, and fBc as the input parameters to determine the light-front meson wave functions, we obtain that fD∗,Ds∗,B∗,Bs∗,Bc∗=(252.0−11.6+13.8, 318.3−12.6+15.3 , 201.9−41.4+43.2, 244.2±7.0, 473.4±18.2) and (264.9−9.5+10.2, 330.9−9.0+9.9, 220.2−46.2+49.1, 265.7±8.0, 487.6±19.2) MeV with Gaussian and power-law wave functions, respectively, while fD2∗,Ds2∗,B2∗,Bs2∗= (143.6−21.8+24.9, 209.5−24.2+29.1, 80.9−27.7+33.8, 109.7−15.0+15.7) MeV with only Gaussian wave functions.