Fractional derivative is a generalization of ordinary derivative with non-integer or fractional order. This research presented fractional derivative of hyperbolic function (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cotangent, hyperbolic secant, and hyperbolic cosecant) with order constraint . The hyperbolic function is presented in Maclaurin series form. Then, the fractional derivative can be determined by using definition of Riemann-Liouville fractional derivative. The result is simulated by using Matlab software