  The low-temperature conductance (G) characteristics between a normal metal
and a clean superconductor (S) carrying a supercurrent $I_s$ parallel to the
interface is theoretically investigated. Increasing $I_s$ causes lowering and
broadening of (1) coherence peaks of s-wave S, and d-wave S at (100) contact,
(2) midgap-states-induced zero-bias conductance peak for d-wave S at (110)
contact, and (3) Andreev-reflection-induced enhancement of $G$ within the gap
near the metallic-contact limit. Novel features found include a current-induced
central peak and a three-humped structure at intermediate barrier strength,
etc.
