We have characterized a strange attractor with a fractal dimension in a fully-developed turbulent channel flow simulated numerically by computing the Lyapunov dimension based on a spatial correlation concept. Our paper presents an example along the line of current discussions whether we can represent an infinite-dimensional dynamical system (fluid flow) by a small finite-dimensional dynamical system. At least for this particular flow under the specified conditions, we can indeed approximate the fluid system by a small-dimensional dynamical system.