The pulsar timing residuals induced by gravitational waves from non-evolving single binary sources with general elliptical orbits are analyzed.For different orbital eccentricities,the timing residuals present different properties.The standard deviations of the timing residuals induced by a fixed gravitational wave source are calculated for different values of the eccentricity.We also analyze the timing residuals of PSR J0437-4715 induced by one of the best known single gravitational wave sources,the supermassive black hole binary in the blazar 0J287.