Synchronous Gaussian code-division multiple access (CDMA) systems employing group-orthogonal signature waveforms are proposed and analyzed. All users in the system are divided into groups of users. The signature waveforms are constructed such that all the signature waveforms in one group are orthogonal to all the signature waveforms used in all other groups. This construction of signature waveforms ensures that there is no inter-group interference (i.e., among users in different groups), but at the expense of having intra-group interference (i.e., among users in the same group). However, by choosing a small size for each group, the intra-group interference can be effectively handled by a low-complexity, optimal (or suboptimal) multiuser detector. It is shown that a significant improvement in the system capacity can be achieved by the proposed technique over the conventional one that uses signature waveforms constructed from Welch-bound-equality (WBE) sequences. In particular, it is demonstrated that, while the conventional system's error performance is very sensitive to even small amount of overload, the proposed system with an appropriate design of signature waveforms can achieve a much higher overload (up to 300% as shown in the paper) with an excellent error performance.