A new class of solutions for Einstein's field equations representing a static spherically symmetric anisotropic distribution of matter is obtained on the background of pseudo-spheroidal spacetime. We have prescribed the bounds of the model parameters k and p(0) on the basis of the elementary criteria for physical acceptability, viz., regularity, stability and energy conditions. By taking the values of model parameters from the prescribed bounds, we have shown that our model is compatible with the observational data of a wide variety of compact stars like 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, PSR J1614-2230, SMC X-4 and Cen X-3.
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