Carbon was known to be one of effective additives which can improve the flux pinning of $MgB_2$ at high magnetic fields. In this study, glycerin $(C_3H_8O_3)$ was selected as a chemical carbon source for the improvement of critical current density of $MgB_2$. In order to replace some of boron atoms by carbon atoms, the boron powder was heat-treated with liquid glycerin. The glycerin-treated boron powder was mixed with an appropriate amount of magnesium powder to $MgB_2$ composition and the powder pallets were heat treated at $650^{circ}C;and;900^{circ}C$ for 30 min in a flowing argon gas. It was found that the superconducting transition temperature $(T_c)$ of $Mg(B_{1-x}C_x)_2$ prepared using glycerin-treated boron powder was 36.6 K, which is slightly smaller than $T_c$(37.1 K) of undoped $MgB_2$. The critical current density $(J_c)$ of $Mg(B_{1-x}C_x)_2$ was higher than that of undoped $MgB_2$ and the $T_c$ improvement effect was more remarkable at higher magnetic fields. The $T_c$, decrease and $J_c$ increase associated with the glycerin treatment for boron powder was explained in terms of the carbon substitution to boron site.