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In this paper, we develop a new relativistic compact stellar model for a spherically symmetric anisotropic matter distribution. The model has been obtained through generating a new class of solutions by invoking the Tolman {\em ansatz} for one of the metric potentials $g_{rr}$ and a physically reasonable selective profile of radial pressure. We have matched our obtained interior solution to the Schwarzschild exterior spacetime over the bounding surface of the compact star. These matching conditions together with the condition of vanishing the radial pressure across the boundary of the star have been utilized to determine the model parameters. We have shown that the central pressure of the star depends on the parameter $p_0$. We have estimated the range of $p_0$ by using the recent data of compact stars 4U 1608-52 and Vela X-1. The effect of $p_0$ on different physical parameters e.g., pressure anisotropy, the subliminal velocity of sound, relativistic adiabatic index etc. have also been discussed. The developed model of the compact star is elaborately discussed both analytically and graphically to justify that it satisfies all the criteria demanded a realistic star. From our analysis, we have shown that the effect of anisotropy becomes small for higher values of $p_0$. The mass-radius (M-R) relationship which indicates the maximum mass admissible for observed pulsars for a given surface density has also been investigated in our model. Moreover, the variation of radius and mass with central density has been shown which allow us to estimate central density for a given radius (or mass) of a compact star.