This work presents the design of a position-sensitive detector that we are evaluating for cosmic-ray muon imaging. The position-sensitive detector consists of an EJ-200 plastic scintillator panel that is 32 × 32 × 2.5 cm in dimension. A quantity of 32 parallel grooves, each 2 mm wide and 4 mm deep with a pitch of 1 cm, are carved on the top and bottom sides, in perpendicular orientation, of a scintillator panel. Two wavelength shifting optical fibers are embedded in each groove for light collection and transport. The optical fibers from each channel are coupled to one pixel of a Hamamatsu H8500C multi-anode photomultiplier tube. An encoding technique using a one-dimensional resistor network was developed to reduce the number of required readout channels for position determination. The position calibration was performed with a blue light emitting diode. The detector was shown to achieve position resolution of ~1 cm (sigma).