In this work, we investigate the lubrication process of a slipper bearing. The slipper bearing consists of two coaxial cylinders in relative motion, where an incompressible micropolar fluid (lubricant) is injected in a thin gap between them. We compute the asymptotic approximation of the solution to the governing micropolar system as a power series in terms of the small parameter ε representing the thickness of the shaft. The proposed approximation is given in the explicit form, allowing us to clearly observe the effects of the micropolar nature of the fluid.