We experimentally reveal the emergence of edge states in a photonic lattice with orbital bands. We use a two-dimensional honeycomb lattice of coupled micropillars whose bulk spectrum shows four gapless bands arising from the coupling of p-like photonic orbitals. We observe zero-energy edge states whose topological origin is similar to that of conventional edge states in graphene. Additionally, we report novel dispersive edge states in zigzag and armchair edges. The observations are reproduced by tight-binding and analytical calculations, which we extend to bearded edges. Our work shows the potentiality of coupled micropillars in elucidating some of the electronic properties of emergent two-dimensional materials with orbital bands.