Three-dimensional limit analysis was utilized to determine the stability of the convex corner in a slurry-supported trench. Analytical solutions were derived for the safety factor of the convex corner stability in a slurry-supported trench. The failure surface has the shape of logarithm helicoids, with outline profile defined by a log-spiral curve. Power expressions were obtained for dissipation rate, gravity and slurry pressure. By solving the energy balance equation, the equation of safety factor for convex corner stability was obtained. The slurry weight ratio, the slurry surface depth, the angle of internal friction and other parameters were discussed. The result indicates that the stability factor increases with increasing slurry and soil bulk density ratio, cohesion, friction angle, but it decreases with decreasing slurry level depth and trench depth ratio, trench width and depth ratio.