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Young's modulus, failure strength, and failure strain of precracked graphene are investigated via finite element method based on molecular structure mechanics in this research. The influence of distribution, length, and orientation of precrack and graphene sizes on these mechanical properties is analyzed. The ratio of precrack length and graphene width is defined as P value, and its particular value Pc can be found, at which the variation trends of Young's modulus, failure strength, and strain have changes with increasing P value. In addition, the fracture toughness of precracked graphene is investigated, and the stress intensity factor (SIF) is calculated according to the Griffith criterion in classical fracture mechanics. The numerical values of the SIF are about 3.20-3.37 MPa√m, which are compared with the experimental results, and the simulations verify the applicability of the classical fracture mechanics to graphene. [ABSTRACT FROM AUTHOR]