This paper presents a new iterative multiuser (MU) detection algorithm for asynchronous spectrally-efficient continuous-phase modulation in additive white Gaussian noise. The proposed detector is derived from the sum-product (SP) algorithm and the factor graph (FG) framework, and performs approximate maximum a posteriori bit detection. A convenient FG of the actual MU detection problem is considered, rather than only FGs of the individual single-user detection problems combined with ad-hoc inter-user interference cancellation. A suitable set of SP messages is approximated by a Gaussian distribution; this considerably reduces the computational complexity and memory size requirements as compared to a straightforward application of the SP rules. The resulting algorithm succeeds in achieving a good error performance.