A numerical solution of the effect of small but fluctuating gravitational field, characteristic of g-jitter, on the free convection boundary layer flow near a three-dimensional stagnation point of attachment resulting from a step change in its surface temperature and immersed in a micropolar fluid is presented in this paper. The case when the spin gradient on the wall is zero (strong concentration of the microelements) is considered. The transformed non-similar boundary layer equations are solved numerically using an implicit finite-difference scheme known as the Keller-box method to investigate the effects of variations in the forcing amplitude parameter, epsilon, forcing frequency parameter, Omega, curvature ratio parameter, c, and micropolar parameter, K, on the skin friction and on the rate of heat transfer. The results are given for a value of the Prandtl number Pr = 0 .72. It has been found that these parameters affect considerably the considered flow and heat transfer characteristics. The comparison with earlier results for a Newtonian fluid (K = 0) is shown to be very good.