We demonstrate Gaussian-shaped phase matching of a periodically-poled potassium titanyl phosphate (PPKTP) crystal by imposing a custom duty-cycle pattern on its grating structure while keeping the grating period fixed. The PPKTP's phase-matching characteristics are verified through optical difference-frequency generation measurements, showing good agreement with expected values based on our design parameters. Our theoretical analysis predicts that under extended phase-matching conditions the custom-poled PPKTP crystal is capable of generating heralded single photons with a spectral purity of 97%, and can reach as high as 99.5% with gentle spectral filtering, something that is highly desirable for photonic quantum information processing applications.