This paper presents a neuro-adaptive finite-time control strategy for uncertain nonstrict-feedback fractional-order nonlinear systems with multiple-objective constraints. To stabilize the uncertain nonlinear fractional-order systems, neural networks (NNs) are employed to identify the unknown nonlinear functions, and dynamic surface control is used to avoid the computational complexity of the backstepping design procedure. The effect caused by the algebraic loop problem can be solved via establishing fractional-order adaptive laws. Introducing a new barrier function, the system output is always limited to the predefined time-varying acceptable range while effectively solving the multi-objective constraint problem. Utilizing fractional-order finite-time stability theory, a finite-time control scheme is constructed to drive the system output to the reference signal in finite time, which ensures better tracking performance. Two examples are given to illustrate the availability and superiority of the presented control scheme.