The s=1/2 quasi-one-dimensional Heisenberg antiferromagnetic chain with asymmetrical sublattices possesses three branches of spin-wave spectra (one in acoustic mode and the other two in optical mode). The frustration relieves the gap-degeneracy of two optical branches and softens the spectrum in acoustic mode, but doesn't soften the spectra in optical mode. Also, the frustration moves down obviously one of the two spectra in optical mode. It means that the frustration makes the spin-wave excitation described by spectrum in optical mode easier and more important. The status of spin on the chain changes more easily than that of side spin under the effect of frustration. The weakening of magnetic order in ground state becomes strong with the strengthening of frustration. By comparison with numerical results of exact diagonalization and DMRG methods, we discuss the merit and drawbacks of the spin-wave approximation.