In 2005 Stakhov and Rozin introduced a new class of hyperbolic functions which is called Fibonacci hyperbolic functions. In this paper, we study q-analogue of Fibonacci hyperbolic functions. These functions can be regarded as q extensions of classical hyperbolic functions. We introduce the q-analogue of classical Golden ratio as follow φq = 1+1+4qn−22, n ≥ 2. Making use of this q-analogue of the Golden ratio, we defined sin Fqh(x) and cos Fqh(x) functions. We investigated some properties and gave some relationships between these functions.