In 1971, integral form of spherical curve in 3-dimensional Euclidean space  was given in [3]. The explicit characterization of the spherical curves in n-dimensional Euclidean space was  given in [12]. Morever, the position vector of spherical curves in Euclidean 3-space was determined in [10]. In the present  work, a)  it is given the system of differential equations of the spherical curves in 3-dimensional Euclidean space; b) it is shown that the numerical solutions of this system of differential equations are obtained in the truncated Taylor series form by using Taylor matris collocation method; c) an example together with error analysis are given to demonstrate the validity and applicability of present  method.