The authors study the Lagrangian stability for the sublinear Duffing equations(x)+e(t)丨x丨α-1x = p(t)with 0＜α＜1,where e and p are real analytic quasi-periodic functions with frequency ω.It is proved that if the mean value of e is positive and the frequency ω satisfies Diophantine condition,then every solution of the equation is bounded.