In this paper,we construct a general class of Stochastic Runge-Kutta(SRK) methods for solving noncommutative stochastic differential equations of It type.The colored rooted tree analysis is applied to drive conditions for coefficients of SRK methods with strong order 1 and minimum principal local truncation error.We present two three-stage explicit SRK (SRKI2v1 and SRKI3v1) methods which have better numerical behaviour than extant methods.Numerical results illustrate the theoretical findings.