By the iteration of the KAM, the following second- order differential equation （ Фp （x′））′ ＋ F（x, x′, t） ＋ ω^PФp （x′） ＋α│x│^l ＋e（x, t） =0 is studied, where Фp（S） = │S│^p-2s, p 〉 1, α〉 0 and ω 〉 0 are positive constants, and l satisfies - 1 〈ω 〈p ＋ 2. Under some assumptions on the parities of F（x, x′, t） and e （x, t）, by a small twist theorem of reversible mapping, the existence of quasi-periodic solutions and boundedness of all the solutions are obtained.
