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Abstract We present herein a new class of singularity-free interior solutions to describe realistic anisotropic compact stellar objects with spherically symmetric matter distribution. A specific form of anisotropy is assumed to obtain the exact solution for the field equation. Smooth matching of interior solutions thus obtained with the Schwarzschild exterior metric over the bounding surface of a compact star, together with the condition that the radial pressure vanishes at the boundary, is used to obtain the mathematical form for the model parameters. The pulsar 4U1608-52 with its current estimated data (mass  $$=1.57 ~M\odot $$ = 1.57 M ⊙ and radius $$=9.8 \pm 0.8$$ = 9.8 ± 0.8  km; Özel et al. in ApJ 820:28, 2016) is used to study the model graphically.