In this paper, we propose a novel rateless multiple access scheme based on the recently proposed capacity-approaching analog fountain code (AFC). We show that the multiple access process will create an equivalent analog fountain code, referred to as the multiple access analog fountain code (MA-AFC), at the destination. Thus, the standard belief propagation (BP) decoder can be effectively used to jointly decode all the users. We further analyse the asymptotic performance of the BP decoder by using a density evolution approach and show that the average log-likelihood ratio (LLR) of each user's information symbol is proportional to its transmit signal to noise ratio (SNR), when all the users utilize the same AFC code. Simulation results show that the proposed scheme can approach the sum-rate capacity of the Gaussian multiple access channel in a wide range of signal to noise ratios.