We propose a correlated spin-singlet-pair wave function to describe the spin-gap phase of the one-dimensional t-J model at low density and large J/t. In addition to having singlet pairs, this wave function has a Jastrow factor with a variational parameter nu. Several correlation functions are calculated by using the variational Monte Carlo method. The result shows the expected long-range behavior of the Luther-Emery phase with the Luttinger exponent K-rho, related to nu, K-rho=1/2 nu.