The main challenge in visible light communications (VLC) is the low modulation bandwidth of light-emitting diodes (LEDs). This forms a barrier towards achieving high data rates. Moreover, the implementation of high order modulation schemes is restricted by the requirements of intensity modulation (IM) and direct detection (DD), which demand the use of real unipolar signals. In this paper, we propose a novel amplitude, phase and quadrant (APQ) modulation scheme that fits into the IM/DD restrictions in VLC systems. The proposed scheme decomposes the complex and bipolar symbols of high order modulations into three different symbols that carry the amplitude, phase and quadrant information of the intended symbol. The constructed symbols are assigned different power levels and are transmitted simultaneously, i.e. exploiting the entire bandwidth and time resources. The receiving terminal performs successive interference cancellation to extract and decode the three different symbols, and then uses them to decide the intended complex bipolar symbol. We evaluate the performance of the proposed APQ scheme in terms of symbol-error-rate and achievable system throughput for different setup scenarios. The obtained results are compared with generalized spatial shift keying (GSSK). The presented results show that APQ offers a higher reliability compared to GSSK across the simulation area, while providing lower hardware complexity.