Performance improvement of the DS-CDMA system by the spectrum-overlap is important for better service quality or more system capacity. In this paper, an analysis thor capacity improvement is newly considered when the Lanczos chip waveform is used for the spectrum-overlapped DS-CDMA system. RC(relative capacity) is the ratio of the capacity of overlapping system to that of non-overlapping system, which is used for the expression of the capacity improvement. The optimal overlapping ratio is numerically found to make the maximum capacity improvement When the rectangular chip waveform is used far the overlapping system, maximum capacity improvement is increased by about 10% at the required BER=$10^{-3}$ and the optimal overlapping ratio is 1.23. When the 95 % power bandwidth is considered for the Lanczos chip waveform, maximum capacity improvement is increased by 34.4% at overlapping ratio of 1.55 when the required BER is $10^{-3}$TEX>. The lower required BER far the better communication quality makes gradually smaller capacity improvement.