In this paper, we present a time-delay estimation algorithm in a closely spaced multipath environment for a direct-sequence code division multiple access (DS-CDMA) systems. The proposed scheme first converts the observed signal to the frequency domain by Fast Fourier Transform (FFT). We then formulate a nonlinear estimation problem, and convert it into a large scale linear least squares problem. We apply conjugate gradients iterations on the resulting normal equations to obtain the solution. Unlike the methods which invoke the criterion of nonlinear least squares, the proposed scheme can achieve higher resolution. The delay estimation is combined with a tracking algorithm based on a FIR prefilter. Simulation results confirm the effectiveness of the proposed algorithm in both AWGN and Rayleigh fading channels.