Controlled spin transport in magnetic stacks is required to realize pure spin current-driven logic and memory devices. The control over the generation and detection of the pure spin current is achieved by tuning the spin to charge conversion efficiency of the heavy metal interfacing with ferromagnets. Here, we demonstrate the direct tunability of spin angular momentum transfer and thereby spin pumping, in CoFeB/Pt stack, with interfacial magnetic anisotropy. The ultra-low thickness of the CoFeB thin film by tilting the magnetization from in-plane to out-of plane direction due to interfacial anisotropy from higher thickness of CoFeB thin film. The ferromagnetic resonance measurements are performed to investigate the magnetic anisotropy and spin pumping in CoFeB/Pt stacks. We clearly observe tunable spin pumping effect in the CoFeB/Pt stacks with varying CoFeB thicknesses. The spin current density, with varying ferromagnetic layer thickness, is found to increase from 1.10MA/m2 to 2.40MA/m2, with increasing in-plane anisotropy field. Such interfacial anisotropy-controlled generation of pure spin current can potentially lead to next-generation anisotropic spin current-controlled spintronic devices.