Abstract: Aiming at bifurcations of limit cycles of a cubic Kolmogorov predator-prey system at the positive equilibrium point (1,1), the real system is translated gradually into a complex system by the computer algebra system Mathematica, then the first five singular point values for the concomitant complex system are calculated, and the numbers of limit cycles at the positive equilibrium point can be deduced by Jacobi determinant. Five small amplitude limit cycles bifurcating from the positive equilibrium point can be concluded in the certain conditions.