Recently, adaptive multi-user detection techniques for interference suppression in direct-sequence code-division multiple-access (DS-CDMA) systems have gained much attention since they do not require any information on interfering users. In the uplink of DS-CDMA systems, however, the base station receiver typically knows the spreading waveforms of the users within its cell but does not know those of the users in other cells. In this paper, we propose a partial zero-forcing adaptive minimum mean squared error (MMSE) receiver for the DS-CDMA uplink utilizing the spreading waveforms known at the base station as well as training data. The proposed receiver first removes the intracell interference using a linear filter based on the knowledge of the spreading waveforms of the interfering users within the cell. Then the intercell interference remaining in the output of the linear filter is mitigated by adaptive MMSE detection. To speed up the convergence of the adaptive filter weights without loss of the steady-state performance, we develop a modified least mean square (LMS) algorithm based on the canonical representation of the filter weights. It is shown through analysis and simulation results that the proposed receiver improves the convergence speed and the steady-state performance.