According to the invention, there is provided a novel soybean variety designated RJS34003. This invention thus relates to the seeds of soybean variety RJS34003, to the plants of soybean RJS34003 to plant parts of soybean variety RJS34003 and to methods for producing a soybean plant produced by crossing plants of the soybean variety RJS34003 with another soybean plant, using RJS34003 as either the male or the female parent.