This article investigates the cooperative control of complex nonlinear multiagent systems (CNMASs), in which the agents suffer from nonaffine faults and the control directions of some agents are unknown. A finite-time adaptive control scheme is presented for the CNMASs. A finite-time command filter is designed to solve the "explosion of complexity" issues, overcome chattering issues, and relax the limitations of the filter input. The impact of filter errors is alleviated by an improved error compensation mechanism. Based on piecewise Nussbaum functions, the partially unknown control direction is addressed. The proposed finite-time cooperative control strategy on the basis of local information can ensure that all signals in the closed-loop system are finite-time bounded, and the absolute value of the cooperative control errors can converge to a given upper bound in a finite time. The rapidity and robustness of the proposed method are verified by two comparative simulation examples. A real multirobot cooperative control experiment is used to verify the effectiveness of the presented method.