Both　pure　and　nano-SIC　doped　MgB2　bulk　samples　were　prepared　by　a　rapid　process.　The　effects　of　fast　heating-up　and　doping　on　the　critical　current　densities　were　studied.　All　samples　were　examined　using　XRD,　SEM　and　magnetization　measurement.　Both　pure　and　doped　samples　show　higher　critical　current　densities　and　irreversible　field　H-irr　compared　with　samples　sintered　at　the　same　temperature　by　a　slow　process.　Experimental　results　manifest　that　fast　heating-up　is　effective　in　reducing　the　grain　size.　This　rapid　process　may　be　preferable　to　avoid　grain　size　enlarging　when　element　substitution　can　be　achieved　only　at　relatively　high　temperatures.