A　long-standing　conjecture　asserts　that　there　is　a　positive　constant　c　such　that　every　n-vertex　graph　without　isolated　vertices　contains　an　induced　subgraph　with　all　degrees　odd　on　at　least　cn　vertices.　Recently,　Ferber　and　Krivelevich　confirmed　the　conjecture　with　c　＞=　10(-4).　However,　this　is　far　from　optimal　for　special　family　of　graphs.　Scott　proved　that　c　＞=　(2　chi)(-1)　for　graphs　with　chromatic　number　chi　＞=　2　and　conjectured　that　c　＞=　chi(-1).　Partial　tight　bounds　of　c　are　also　established　by　various　authors　for　graphs　such　as　trees,　graphs　with　maximum　degree　3　or　K-4-minor-free　graphs.　In　this　paper,　we　further　prove　that　c　＞=　2/5　for　planar　graphs　with　girth　at　least　7,　and　the　bound　is　tight.　We　also　show　that　c　＜=　1/3　for　general　planar　graphs　and　c　＞=　1/3　for　planar　graphs　with　girth　at　least　6.