We consider the following fractional Choquard equation with critical or supercritical growth where s \in (0, 1), \mu\in (0, N), N>2s, q\geq 2_{\mu, s}^\ast, f is a continuous function. It is well-known that 2_{\mu, s}^\ast=\frac{2N-\mu}{N-2s} and 2_{\mu, s}=\frac{2N-\mu}{N} are critical exponents for the above equation in the sense of Hardy-Littlewood-Sobolev inequality. Many existence results have been established for q \in[2_{\mu, s}, 2_{\mu, s}^\ast] in recent years. Here we are interested in critical or supercritical case for the above equation. Under some assumptions of f, the existence and multiplicity of solutions for the above equation can be obtained by applying some analytical techniques.