The financial problems often relate to many stochastic differential equations which is difficult to solve. Based on the traditional numerical methods for solving determinate ordinary differential equations (ODEs), the paper presents the numerical methods of stochastic ordinary differential equations (SODEs). The numerical methods mainly considered in the paper include Euler method and Euler method discusses three numerical schemes, i.e. explicit scheme, semi-implicit scheme and implicit scheme. Finally, the paper uses Euler methods to simulate linear stochastic ordinary differential equation. Numerical results indicate that Euler methods are the simple but have a certain practicality. In addition, all these Euler method including explicit, semi-implicit and implicit scheme in this paper can be applied to high-order stochastic ordinary differential equations, stochastic partial differential coefficient equations, and so on.