Trapping technologies of positrons, the antimatter counterpart of electrons, are indispensable for various atomic, molecular, and optical experiments and for material analyses that use positron swarms. Efficient trapping of high-intensity positron beams generated by electron linear accelerators (LINACs) will improve the quality and throughput rate of experiments but have yet to be practically realized. In the present work, we demonstrate the efficient trapping and extraction of a LINAC-based positron beam by using a silicon carbide (SiC) remoderator with a centre hole. The positron beam was remoderated by 4H-SiC wafers in the back-reflection geometry followed by accumulation in an electromagnetic trap with CF4 cooling gas. A rotating electric field was driven to spatially compress the accumulated positrons, enabling the lossless extraction of the positrons through the SiC hole. A trapping efficiency in the higher 20% range was achieved. The proposed trapping scheme employing a centre-hole SiC remoderator is thus a practical technique to accumulate and cool positron beams generated by LINACs.