The study of Hawking radiation of fermions via tunneling is a hot spot of current topics in black hole physics. By constructing a set of appropriate matrices γμ for general covariant Dirac equation, the tunneling effect of Kaluza-Klein spacetime was deeply studied. For spacetimes with different dimensions, constructing a set of appropriate γμ matrices for general covariant Dirac equation is an important technique for fermions tunneling method. As a result, the tunneling probability of Dirac particles and the expected Hawking temperature of the spacetime were successfully recovered.