With the motivation to study how non-magnetic ion site disorder affects the quantum magnetism of Ba3CoSb2O9, a spin-1/2 equilateral triangular lattice antiferromagnet, we performed DC and AC susceptibility, specific heat, elastic and inelastic neutron scattering measurements on single crystalline samples of Ba2.87Sr0.13CoSb2O9 with Sr doping on non-magnetic Ba2+ ion sites. The results show that Ba2.87Sr0.13CoSb2O9 exhibits (i) a two-step magnetic transition at 2.7 K and 3.3 K, respectively; (ii) a possible canted 120-degree spin structure at zero field with reduced ordered moment as 1.24{mu}B/Co; (iii) a series of spin state transitions for both H // ab-plane and H // c-axis. For H // ab-plane, the magnetization plateau feature related to the up-up-down phase is significantly suppressed; (iv) an inelastic neutron scattering spectrum with only one gapped mode at zero field, which splits to one gapless and one gapped mode at 9 T. All these features are distinctly different from those observed for the parent compound Ba3CoSb2O9, which demonstrates that the non-magnetic ion site disorder (the Sr doping) plays a complex role on the magnetic properties beyond the conventionally expected randomization of the exchange interactions. We propose the additional effects including the enhancement of quantum spin fluctuations and introduction of a possible spatial anisotropy through the local structural distortions.