Microsphere arrays can be used to effectively detect, identify, and quantify biological targets, such as mRNAs, proteins, antibodies, and cells. In this work, we design a microfluidic microsphere-trap array device that enables simultaneous, efficient, and accurate screening of multiple targets on a single platform. Different types of targets are captured on the surfaces of microspheres of different sizes. By optimizing the geometric parameters of the traps, the trap arrays in this device can immobilize microspheres of different sizes at different regions with microfluidic hydrodynamic trapping. The targets are thus detected according to the microspheres' positions (position-encoding), which simplifies screening and avoids errors in target identification. We validate the design using fluid dynamics finite element simulations by COMSOL Multiphysics software using microsphere of two different sizes. We also performed preliminary microspheretrapping experiments on a fabricated device using microspheres of one size. Our results demonstrate that the proposed device can achieve the position-encoding of the microspheres with few fluidic errors. This device is promising for simultaneous detection of multiple targets and become a cheap and fast disease diagnostic tool.