Recently, the single photon avalanche diode optical wireless communication (SPAD OWC) has attracted much attention due to its potential underwater applications. For such system, the channel noise is additive Poisson noise (APN) rather than the commonly encountered additive white Gaussian noise (AWGN) and the corresponding maximum likelihood (ML) detection is hard to provide a useful insight into energy-efficient signal design. By using the previously proposed Hellinger distance design criterion, we design an energy-efficient multi-dimensional constellation within the nonnegative integer set by minimizing the average optical power for a fixed minimum Hellinger distance. Comprehensive simulations indicate that our designed constellation can substantially outperform the currently available pulse amplitude modulation (PAM) and squared PAM for SPAD OWC systems.