In order to compare the size relationship and the equality of private integers from two users without any risk of leaking their secrets, we put forward a novel two-round two-party quantum private comparison (QPC) protocol with a third party (TP) based on one-direction quantum walks on a circle (ODQWC). Here, TP is allowed to launch all kinds of possible attacks except the collusion attack. This protocol adopts quantum walk (QW) states as the initial quantum resource, which are actually a kind of two-particle product states. This protocol doesn’t need any pre-shared secret key or quantum entanglement swapping operation, and only adopts unitary operations andd-dimensional single particle measurements. Security analysis validates the security of the proposed protocol against both the outside attacks and the participant attacks. Compared with previous QPC protocols based on QW, this protocol is more efficient under certain conditions. Moreover, we construct quantum circuits for this protocol and reveal its correctness and feasibility by IBM Qiskit simulator.