The (singular) orthogonal graph *O*(2ν + δ, *q*) over a field with *q* elements and of characteristic 2 (where ν ⩾ 1, and δ = 0, 1 or 2) is introduced. When ν = 1, *O*(2 · 1, *q*), *O*(2 · 1 + 1, *q*) and *O*(2 · 1 + 2, *q*) are complete graphs with 2, *q* + 1 and *q*^{2} + 1 vertices, respectively. When ν ⩾ 2, *O*(2ν + δ, *q*) is strongly regular and its parameters are computed. *O*(2ν + 1, *q*) is isomorphic to the symplectic graph *Sp*(2ν, *q*). The chromatic number of *O*(2ν + ν, *q*) except when δ = 0 and ν is odd is computed and the group of graph automorphisms of *O*(2ν + δ, *q*) is determined.