Given a positive integer \(N\), let \(X_0(N)\) be the modular curve determined by the congruence subgroup \(\Gamma_0(N) \subset \text{SL} (2,\mathbb{Z})\). In this paper, the author describes a general method of calculating defining equations of modular curves \(X_0(N)\) using the Fourier expansion of a certain cusp form of weight two for \(\Gamma_0(N)\). He also lists defining equations of all modular curves \(X_0(N)\) of genus two to six.