This paper proposes MRO-PUF, a new architecture for ring-oscillator-based physically unclonable functions (PUFs) with enhanced resistance against machine learning attacks. In the proposed PUF, an instantaneous output value of a ring oscillator is used as a response, whereas the most existing PUFs directly use propagation delays to determine the response. Since the response of the MRO-PUF is non-linear and discontinuous as the delay of the ring oscillator increases, the prediction of the response by machine learning attacks is difficult. Through the performance evaluation of the MRO-PUF with simulations, it achieves 15 times stronger resistance against machine learning attacks using a support vector machine compared to the existing ones such as an arbiter PUF and a bistable ring PUF. The MRO-PUF also achieves a sufficient level of the basic performance of PUFs in terms of uniqueness and robustness.