In this work, a novel processing technique for patterning of graphene monolayer prepared on various platforms, glass and poly(ethylene terephthalate) (PET) substrates, is suggested and experimented for its validity evaluation. Two process parameters of the Q-switched 1064μm Nd:YVO4 laser system, scanning speed and repetition rate, were controlled for investigating the geometric features of the graphene line patterns and obtaining an optimum process conditions in the given laser system. The differences among line patterns acquired by controlled process conditions and substrate materials have been investigated and the underlying physics is contemplated. Multiple tools were utilized for evaluating the results, which included an optical microscopy for dimension check, Raman analysis, and G- and 2D-peak mapping technique. Continuous graphene line patterns have been successfully obtained from the most of the schemed process conditions and it would be revealed that the laser pattering is a plausible technique for patterning the graphene monolayers in fabricating various electronic and optical devices.