Based on the Lagrange interpolation polynomial algorithm, the error analysis is discussed in this paper. Firstly, we derive the Lagrange interpolation polynomial algorithm and introduce the shape function with the usage of related data figures. Secondly, how to derive the Lagrange interpolation function is also simply introduced. At last, some examples have been given to display the error analysis of the Lagrange interpolation polynomial algorithm and two conclusions are suggested to minimize the errors in Lagrange interpolation.