Radiation pressure in an optomechanical system can be used to generate various quantum phenomena. Recently, one paid more attention to the study of optical nonreciprocity in an optomechanical system, and nonreciprocal devices are indispensable for building quantum networks and ubiquitous in modern communication technology. Here in this work, we study how to realize the perfect optical nonreciprocity in a two-cavity optomechanical system with blue-detuned driving. Our calculations show that the optical nonreciprocity comes from the quantum interference of signal transmission between two possible paths corresponding to the two interactions in this system, i.e. optomechanical interaction and linearly-coupled interaction. According to the standard input-output relation of optical field in cavity optomechanics, we obtain the expression of output optical field, from which we can derive the essential conditions to achieve the perfect optical nonreciprocity, and find there are two sets of coupling strengths both of which can realize the perfect optical nonreciprocal transmission. Because the system is driven by blue-detuned driving, the system is stable only under some conditions which we can obtain according to the Routh-Hurwitz criterion. Due to the blue-detuned driving, there will be transmission gain (transmission amplitude is greater than 1) in the nonreciprocal transmission spectrum. We also find that the bandwidth of nonreciprocal transmission spectrum is in proportion to mechanical decay rate if mechanical decay rate is much less than the cavity decay rate. In other words, in a realistic optomechanical parameter regime, where mechanical decay rate is much less than cavity decay rate, the bandwidth of nonreciprocal transmission spectrum is very narrow. Our results can also be applied to other parametrically coupled three-mode bosonic systems and may be used to realize the state transfer process and optical nonreciprocal transmission in an optomechanical system.