We present the covariant BRST quantization of the super-D-string. The non-vanishing supersymmetric U(1) field strength $\cal F$ is essential for the covariant quantization of the super-D-string as well as for its static picture. A SO(2) parameter parametrizes a family of local supersymmetric (kappa symmetric) systems including the super-D-string with $\cal F\ne 0$ and the Green-Schwarz superstring with $\cal F= 0$. We suggest that $E^1$ (canonical conjugate of U(1) gauge field) plays a role of the order parameter in the Green-Schwarz formalism: the super-D-string exists for $E^1 \ne 0$ while the fundamental Green-Schwarz superstring exists only for $E^1 =0$.