The existing broad learning system （BLS） forms its union nodes by generating a series of mapping nodes and enhancement nodes. Due to the linear connection between the union nodes and the output layer， the weights of the network built by BLS can be obtained quickly by using the corresponding pseudo-inverse computation， thus avoiding the time-consuming training process. As a result， BLS becomes very fast and efficient. However， in order to achieve satisfactory performance， BLS quite often needs too many enhancement nodes， which may cause over-fitting phenomenon. A functional-link neural network （FLNN） based deep classifier， called FLNNDC， is proposed to circumvent the above drawback. FLNNDC stacks several lightweight BLS sub-systems into a stacked structure， while each lightweight BLS sub-system is built by generating enhancement nodes from randomly selected mapped features instead of all the mapped features. Experimental results on several popular datasets demonstrate the effectiveness of FLNNDC in the sense of both downsized structure and less running time.