The purpose of the present study is to examine the heat transport limitations in a screen mesh heat pipe for electronic cooling by theoretical analysis. Diameter of pipe was 6mm, and mesh numbers were 50, 100, 150, 200 and 250, and water was investigated as working fluid. According to the change of mesh number, wick layer, inclination and saturation temperature, the maximum heat transport limitations by capillary, entraintment, sonic and boiling were analyzed by a theoretical design method of heat pipe, including capillary pressure, pumping pressure, liquid friction coefficient in wick, vapor friction coefficient, etc. Based on the results, the capillary limitation in a small diameter of heat pipe is largely affected by mesh number and wick layer. Mesh number of 250 is desirable not to be used in pipe diameter of 6 mm, because capillary heat transport limitation decreases by the abrupt increase of liquid friction pressure due to the small liquid flow area. For the heat transport of 15 watt in 6mm diameter pipe, mesh number of 100 and one layer is an optimum wick condition, which thermal resistance is the smallest.