The design, fabrication, and demonstration of a novel Silicon Carbide Low Gain Avalanche Detector (4H-SiC LGAD), exhibiting an ultra-fast time response and excellent time resolution, are reported. The use of field plates is proposed to suppress the high electric field caused by the negative bevel-etched angle in 4H-SiC LGADs based on TCAD simulations. Experimental measurements confirm that the field plate significantly increases the breakdown voltage of the 4H-SiC LGADs. Gain and time resolution are measured by using the ultraviolet transient current technique (UV-TCT) showing that 4H-SiC LGADs possess excellent timing performance, with a time resolution better than 35 ps for the injected laser signal with single minimum ionizing particle (MIP) charges generation at room temperature. Additionally, the gain suppression effect in a 4H-SiC LGAD is observed for the first time.