To　obtain　a　constant　gradient　magnetic　field　outside　unilateral　nuclear　magnetic　resonance　(NMR),　optimal　design　method　based　on　finite　element　method　(FEM)　and　topology　optimization　is　proposed.　Topology　design　sensitivity　in　terms　of　design　variables　of　permanent　magnetic　system　is　derived　analytically　using　the　adjoint　variable　method.　Then　coupled　with　continuum　topology　sensitivity　analysis,　penalty-function　method　is　employed　to　find　an　optimized　distribution　of　the　direction　of　magnetization　of　the　permanent　magnets　of　unilateral　NMR.　Numerical　study　shows　the　effectiveness　of　the　proposed　optimal　design　method.