In this research, the free vibration of graphene origami auxetic metamaterial nanobeams is investigated using Eringen's nonlocal elasticity theory and Euler-Bernoulli beam theory. Graphene origami-reinforced nanobeams exhibit auxetic behavior due to their specific geometric structure, which includes folding patterns at the nanoscale. This behavior arises from the gradual unfolding of graphene folds under tension, causing lateral expansion of the material, and consequently, unlike conventional materials, it expands in the direction perpendicular to the applied force. The effective material properties including Young's modulus, density, and Poisson's ratio are calculated using homogenization relations and correction functions dependent on temperature and folding degree. The governing equations are derived using the energy method, space-time separation, generalized Lagrange equations, and natural frequencies are extracted by solving the eigenvalue problem. The dimensionless natural frequencies of the simply-supported nanobeam are validated against existing studies. The results indicate that increasing the weight percentage of graphene origami increases the natural frequency of the nanobeam due to the increase in Young's modulus and decrease in density. Furthermore, increasing the folding degree, while enhancing the auxetic property, reduces the natural frequency due to the decrease in Young's modulus. Increasing the nanobeam length due to increased mass and also increasing the nonlocal parameter due to reduced effective stiffness of the beam lead to a decrease in the natural frequency.