Focusing on the conservation properties, the symplectic Euler scheme of the harmonic oscillator was constructed to analyze its vibration properties. Firstly, three conservation laws, including the square conservation law, the period conservation law and the phase difference conservation law, were presented for the harmonic oscillator. And then, the common Euler scheme and the symplectic Euler scheme were constructed to study the above three conservation laws. The numerical results imply that the symplectic Euler scheme can preserve the conservation law in time domain (the square conservation law) exactly, but can’t preserve the conservation laws in phase domain (the period conservation law and the phase difference conservation law), which is the shortcoming of the symplectic method but can be overcome by the modification method presented by Prof. Xing.