This paper proposes low complexity resource allocation in frequency domain non-orthogonal multiple access where many devices access with a base station. The number of the devices is assumed to be more than that of the resource for network capacity enhancement, which is demanded in massive machine type communications (mMTC). This paper proposes two types of resource allocation techniques, all of which are based on the MIN-MAX approach. One of them seeks for nicer resource allocation with only channel gains. The other technique applies the message passing algorithm (MPA) for better resource allocation. The proposed resource allocation techniques are evaluated by computer simulation in frequency domain non-orthogonal multiple access. The proposed technique with the MPA achieves the best bit error rate (BER) performance in the proposed techniques. However, the computational complexity of the proposed techniques with channel gains is much smaller than that of the proposed technique with the MPA, whereas the BER performance of the proposed techniques with channel gains is only about 0.1 dB inferior to that with the MPA in the multiple access with the overloading ratio of 1.5 at the BER of 10 −4 . They attain the gain of about 10 dB at the BER of 10 −4 in the multiple access with the overloading ration of 2.0. Their complexity is 10 −16 as small as the conventional technique.