Abstract: Quantum error-correcting codes play an important role in not only quantum communication but also quantum computation. Previous work in constructing quantum error-correcting codes focuses on code constructions for symmetric quantum channels, i.e., qubit-flip and phase-shift errors have equal probabilities. This paper focuses on the asymmetric quantum channels, i.e., qubit-flip and phase-shift errors have different probabilities Some present families of asymmetric quantum codes are constructed with classical quadratic residue codes and Reed-Muller codes. Compared to previously known methods, the method is simple. Furthermore, using the Trace map, more asymmetric quantum error-correcting codes are obtained.