The energy conditions of mimetic-f(R) gravity theory, together with the Dolgov-Kawasaki instability will be analysed. It will be shown that the condition for the stability of the theory against Dolgov-Kawasaki is equivalent to the standard f(R) gravity theory. The Brans-Dicke equivalence of the theory is also discussed in more details. We will then obtain the parameter space of the theory in some special forms of f(R), which violates the strong energy condition while satisfying the weak, null and dominant energy conditions.