Near-unity energy transfer efficiency has been widely observed in natural photosynthetic complexes. This phenomenon has attracted broad interest from different fields, such as physics, biology, chemistry and material science, as it may offer valuable insights into efficient solar-energy harvesting. Recently, quantum coherent effects have been discovered in photosynthetic light harvesting, and their potential role on energy transfer has seen heated debate. Here, we perform an experimental quantum simulation of photosynthetic energy transfer using nuclear magnetic resonance (NMR). We show that an N- chromophore photosynthetic complex, with arbitrary structure and bath spectral density, can be effectively simulated by a system with log2 N qubits. The computational cost of simulating such a system with a theoretical tool, like the hierarchical equation of motion, which is exponential in N, can be potentially reduced to requiring a just polynomial number of qubits N using NMR quantum simulation. The benefits of performing such quantum simulation in NMR are even greater when the spectral density is complex, as in natural photosynthetic complexes. These findings may shed light on quantum coherence in energy transfer and help to provide design principles for efficient artificial light harvesting.