We study the evolution of Gravitational Waves (GWs) during and after inflation as well as the resulting observational consequences in a Lorentz-violating massive gravity theory with one scalar (inflaton) and two tensor degrees of freedom. We consider two explicit examples of the tensor mass m_g that depends either on the inflaton field ϕ or on its time derivative ϕ̇, both of which lead to parametric excitations of GWs during reheating after inflation. The first example is Starobinsky's R^2

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... tion model with a ϕ-dependent m_g and the second is a low-energy-scale inflation model with a ϕ̇-dependent m_g. We compute the energy density spectrum Ω_ GW(k) today of the GW background. In the Starobinsky's model, we show that the GWs can be amplified up to the detectable ranges of both CMB and DECIGO, but the bound from the big bang nucleosynthesis is quite tight to limit the growth. In low-scale inflation with a fast transition to the reheating stage driven by the potential V(ϕ)=M^2 ϕ^2/2 around ϕ≈ M_ pl (where M_ pl is the reduced Planck mass), we find that the peak position of Ω_ GW(k) induced by the parametric resonance can reach the sensitivity region of advanced LIGO for the Hubble parameter of order 1 GeV at the end of inflation. Thus, our massive gravity scenario offers exciting possibilities for probing the physics of primordial GWs at various different frequencies.