Anisotropic Compacts Stars on Paraboloidal Spacetime with Linear Equation of State

New exact solutions of Einstein's field equations (EFEs) by assuming linear equation of state, $p_r = \alpha (\rho - \rho_R)$ where $p_r$ is the radial pressure and $\rho_R$ is the surface density, are obtained on the background of a paraboloidal spacetime. By assuming estimated mass and radius of strange star candidate 4U 1820-30, various physical and energy conditions are used for estimating the range of parameter $\alpha$. The suitability of the model for describing pulsars like PSR J1903+327, Vela X-1, Her X-1 and SAX J1804.3658 has been explored and respective ranges of $\alpha$, for which all physical and energy conditions are satisfied throughout the distribution, are obtained.