This paper presents a numerical solution of the one-dimensional Burgers’ equation using a method based on the collocation of radial basis functions (RBF) over a meshless framework. The Burgers’ equation is a typical nonlinear evolutionary partial differential equation, and its numerical solution is of great interest in various fields of applied mathematics and engineering. The proposed method combines the RBF collocation approach with the method of lines (MOL) to semi-discretize the spatial domain and solve the resulting system of ordinary differential equations in time. The accuracy and flexibility of the method are demonstrated through the numerical results of two different examples, showcasing its potential for efficiently and accurately solving the one-dimensional Burgers’ equation.