The theory of Observational Relativity (OR) as a new theory of physics is repored in the form of serial reports in F1000Research. Now, OR Serial Report 4 focuses on re-examining Einstein's prediction on Mercury's perihelion precession from the perspective of OR. In 1916, from general relativity, Einstein derived an equation of planetary motion. Unlike Newton's, Einstein's equation of planetary motion has an additional orbital-precession item based on which Einstein made the famous prediction: Mercury's perihelion precesses by 43.03 arcsec every 100 Earth Years. Einstein's 43.03 arcsec seems to exactly match the 43.11 arcsec left in the history data of Mercury that has not yet found a definite reason. This was an early successful case of Einstein's theory of general theory. The theory of OR has also deduced an equation of planetary motion that also has an additional orbital-precession item. The theory of OR discoveries that such orbital precession purely depends on the speeds of the information waves of observation agents, and that Einstein's orbital-precession item observed with the optical agent is just a special case of the OR orbital-precession item. This fact indicates that Einstein's orbital-precession item does not represent the objective and real precession of planetary orbits. As a matter of fact, Einstein's prediction on Mercury's perihelion precession is a sort of observational effect and apparent phenomenon caused by the observational locality of the optical agent, rather than the objectively real physical existence.