The electric field analytical expression of Laguerre-Gaussian beam under nonparaxial approximation condition is derived based on the vectorial Rayleigh-Sommerfeld diffraction theory. According to this expression, analytical expressions of the orbital angular momentum density under paraxial and nonparaxial approximation conditions are deduced. Through the numerical simulation, the orbital angular momentum density distribution characteristics under paraxial and nonparaxial approximation conditions are studied, and then the effects of topological charge, waist radius and transmission distance on the orbital angular momentum density distribution are analyzed. It is shown that the orbital angular momentum density distribution under the nonparaxial approximation condition is different from that under the paraxial approximation condition, but the shape of the orbital angular momentum density distribution is close to that under the paraxial approximation with the increase of the topological charge. The result also shows that the topological charge, waist radius and transmission distance do not influence the shape of the orbital angular momentum density distribution under the paraxial approximation condition, while the shape and size of the orbital angular momentum density distribution under the nonparaxial approximation condition are affected by the parameters above.