We have investigated crystal growth and critical current densities of MgB2 which was synthesized using stoichiometry or excess Mg and two kinds of B grain size. Excess Mg plays a role not only to promote crystal growth but also to make crystal grains fine. During crystal growth, the critical current densities decrease, although the density remains constant, approximately. Irrespective of the starting B powder, J(CM) is the highest in the sample with the smallest crystal grains and highest density of MgB2. The effects of excess Mg creates the possibility to control crystal size of MgB2 by adjusting the quantity of Mg.