Malicious attack is a potential threat for collision-free and connectivity-preserving formation control. In this paper, a predictor-based collision-free and connectivity-preserving resilient formation control strategy is presented for a class of nonlinear multi-agent systems under sensor deception attacks. The predictor states are designed to replace original states in the control strategy, and a novel attack compensator is constructed to suppress sensor deception attack. Prediction errors, instead of compromised errors, are introduced to update radial basis function neural networks (RBFNNs) weights. To achieve collision avoidance and connectivity preservation, a transformation function in logarithmic form is proposed. To avoid static and dynamic obstacles, an improved artificial potential function (APF) combined with their velocity information is constructed. Furthermore, to solve the local minimum in the combining of transformation function and APF, a virtual force is added to make agents get away. Based on the Lyapunov stability criterion, all closed-loop signals are bounded and all control objectives can be achieved. The simulation of a group of quadrotors has verified the effectiveness of the proposed resilient control strategy.