We designed and evaluated performance of a high resolution large-area detector for positron emission tomography (PET) based on a crystal assembly readout using wavelength-shifting (WLS) fibers, offering a cost-effective alternative to the direct readout of monolithic crystals with photodetectors. The considered detector geometries are made up of 4×4 assembly of LuY2SiO5:Ce (LYSO) crystal scintillators, each with surface area of 50×50 mm2 and thickness 7 or 15 mm optically coupled together using optical adhesive. The crystal assembly is coupled with orthogonal wavelength-shifting (WLS) fibers of square cross-section placed on the top and bottom of the assembly. To evaluate the characteristics of the novel detector we used the GEANT4 to perform optical photon transport in the crystal assembly and WLS fibers. The simulation results show that best position resolution achieved is around 1.6 mm FWHM and 3.8 mm FWTM for crystal thickness 7 mm and 1.5 mm FWHM and 4.8 mm FWTM for crystal thickness 15 mm. Compared to direct photosensor readout, WLS fibers can drastically reduce the number of photosensors required while covering a larger sensitive detection area. In proposed detector design 2N photodetectors are used to cover the same image area instead of N2 with direct readout. This design allows for the development of a compact detector with an expanded effective field of view and reduced cost.