Interference fringes are obtained in a field-emission microscopy (FEM) study of a multi-walled carbon nanotube (MWCNT) with two open-ended branches. The FEM pattern, which is composed of three parallel streaks, can be interpreted by using classical Young's double-slit interference with the ends of the two MWCNT branches treated as two secondary sources of the electron wave. The origin of the coherency of the electron beams from the two branches is discussed on the basis of the quantitative analysis of the FEM pattern. The result suggests a new approach to obtaining a coherent electron source.