[en] With LIGO having achieved its design sensitivity and the LIGO S5 strain data being available, constraints on the relic gravitational waves (RGWs) become realistic. The analytical spectrum of RGWs generated during inflation depends sensitively on the initial condition, which is generically described by the index β, the running index α_t, and the tensor-to-scalar ratio r. By the LIGO S5 data of the cross-correlated two detectors, we obtain constraints on the parameters (β,α_t,r). As a main result, we have computed the theoretical signal-to-noise ratio of RGWs for various values of (β,α_t,r), using the cross-correlation for the given pair of LIGO detectors. The constraints by the indirect bound on the energy density of RGWs by big bang nucleosynthesis and cosmic microwave background have been obtained, which turn out to be still more stringent than LIGO S5.