A research has been conducted on the l1 norm coherence and quantum relative entropy coherence of single quantum bit in Bloch representation, thus obtaining two analytical expressions of coherence for phase damping channel, depolarization channel and amplitude damping channel respectively. As a specific application, an analytical study has been made on the dynamic evolution of quantum coherence of a single quantum bit in an amplitude-damped channel, followed by a numerical analysis of the influences of Markovian as well as non-Markovian environments on the coherence evolution of the system.