The existing multi-directional light-emitting diode (MD-LED) aided visible light positioning (VLP) scheme is difficult to physically implement. An improved MD-LED based VLP scheme is proposed, in which we devise an integrated single lamp that consists of a regular pyramid metal block and multiple standard Lambert radiation light-emitting diode chips, which are mounted on different planes of the metal block. In addition, a localization algorithm exploiting received signal strength ratio based on linear least squares is provided. Simulation and experiment results show that this scheme can achieve an average localization accuracy of 5 and 11 cm, respectively, at a known height in the realistic mobile user scenario with a tilting receiver. Compared with the existing MD-LED aided VLP scheme, this scheme implements the first ever prototype MD-LED lamp and has a low implementation cost.