An adaptive integral sliding mode guidance law with impact angel constraint is proposed for the guidance problem during the maeuvering target interception. Firstly, the nonlinear integral sliding manifold with finite time convergence is designed and the reaching law is given based on the fast terminal sliding mode. Secondly, an adaptive law is proposed to estimate the square of the target maneuvering acceleration bound, based on which the adaptive integral sliding mode guidance law is derived, which possesses the smooth feature. Finally, the finite time convergence of the guidance system both for the reaching phase and on the sliding mold is proved based on the finite stability theory, and the convergence regions of the sliding variable and the system states are derived. Simulation results show the effectiveness of the proposed method.