A bulk silicon carbide single crystal of good crystalline quality which includes a minimized number of structural defects and is free from micropipe defects can be produced by crystal growth in a melt of an alloy comprising Si, C, and M (wherein M is either Mn or Ti) and having an atomic ratio between Si and M in which the value of x, when express as Si1-xMx, is 0.1≦×≦0.7 in the case where M is Mn or 0.1≦×≦0.25 in the case where M is Ti at a temperature of the melt which is below 2000° C. The C component is preferably supplied into the melt by dissolution of a graphite crucible which contains the melt such that the melt is free from undissolved C. One method of crystal growth is performed by cooling the melt after a seed substrate is immersed in the melt.