We study empirical relation between the intrinsic peak energy $E_\mathrm{i,p}$ of the $\nu F_{\nu}$ spectrum and the isotropic peak luminosity ($L_\mathrm{iso}$) of Gamma-ray burst (GRB) prompt emission in the cosmological source frame. The $E_\mathrm{i,p}$ and $L_\mathrm{iso}$ are computed for all long GRBs detected by the Fermi Gamma-ray Burst Monitor (GBM) and Swift-Burst Alert Telescope (BAT) until the end of December 2017, for which redshift is measured and which has a well defined time-integrated peak spectrum. The GBM has larger sky coverage than BAT but is less sensitive, therefore GRBs that trigger GBM are visible to the BAT. It is very interesting to study the $E_\mathrm{i,p}$-$L_\mathrm{iso}$ correlation using the samples obtained from both these detectors because each has its own advantages. In both samples, we found that the $E_\mathrm{i,p}$ is strongly correlated with the $L_\mathrm{iso}$. Using the slope and normalization obtained from our fits, we constructed the Hubble diagram and estimate the cosmological parameters for the GRB samples, and also by combining our GRB samples together with the latest Union Supernovae (SNe) type Ia data.