The detection of the cross-correlation of weak gravitational lensing (WL) and the thermal Sunyaev-Zel'dovich effect (tSZ) has recently been reported by several groups. With this cross-correlation and the power spectrum of tSZ, we address the non-thermal pressure support in galaxy clusters and constrain the amplitude of matter power spectrum, i.e. sigma8. For theoretical predictions, the halo model prescription is employed to explore large parameter spaces. We run cosmological N-body simulations to estimate the covariance matrix. For WL, we employ the ray-tracing technique to create mock 30 WL maps of 100 deg^2. For tSZ, in addition to the distribution of matter, we need to model gas pressure. The spatial distribution of halos are obtained from N-body simulations and then we paste thermal pressure onto each particle by the analytic model or fitted profile by observations. We present and discuss constraints on the property of the non-thermal pressure and sigma8 with the measurements of the Planck mission and RCSLenS.