An apparatus for preventing oil from draining in an engine oil supply system, which supplies the oil from a main gallery in an engine to diverge into a first oil pipe communicating with an intake side hydraulic lash adjuster and into a second oil pipe communicating with an exhaust side hydraulic lash adjuster, may include an adaptor installed between the first oil pipe and a main oil passage connected to the main gallery, wherein the adaptor is disposed higher than the first oil pipe so as to prevent the oil from draining back, and wherein the second oil pipe is communicated with the mail oil passage through a connection pipe.