In this paper, analysis of average bit error ratio (BER) performance of a quadriphase shift keying (QPSK) direct-sequence code-division multiple-access (DS-CDMA) system with narrow-band interference (NBI) suppression complex adaptive infinite-impulse response (IIR) notch filter is presented. QPSK DS-CDMA signal is transmitted over a Rayleigh frequency-nonselective fading channel and the NBI has a randomly-varying frequency. A closed-form expression that relates BER with complex coefficient IIR notch filter parameters, received signal-to-noise ratio (SNR), number of DS-CDMA active users and processing gain is derived. The derivation is based on the Standard Gaussian Approximation (SGA) method. Accuracy of the BER expression is confirmed by computer simulation results.