We propose a unified theory, that is, similarity transformation, to construct exact optical rogue wave solution of (1+1)-dimensional nonlinear Schrödinger equation with variable coefficients. Moreover, we investigate propagation dynamics of the first-order optical rogue wave in an optical fiber amplifier. In the suitable regulation of parameters, we find that the properties of the optical rogue wave, such as width, amplitude and position, are controllable in a nonlinear medium. These results give edification in theory and practical application.