This paper proposes an algorithm for globally approximating real algebraic plane curves of degree k with B-spline curves of the same degree. Each connected component is approximated with a B-spline curve. It is suitable for all irreducible real plane algebraic curves with arbitrary genus (including singular curves). This method is based on our blowup sampling method of algebraic curves, which solves the difficult problem of sampling around singular points in essence. The experimental results show that the algorithm achieves better accuracy than the existed methods.