The influence of slow cooling and annealing time in $O_2$in MPEG process on $J_c$ was investigated. From the measurement of $J_c$,SEM and XRD, it was observed that the critical current density was related with the slow cooling time and annealing time in $O_2$. The value of $J_c$ was the highest at slow cooling time of 40 hour. And also, the value of $J_c$ along the annealing time in $O_2$in the case of the slow cooling time of 40 hours was inclined to increase with annealing time. Consequently, it can be suggested that proper slow cooling time and annealing time after slow cooling in MPMG process be important to improve the critical characteristics.