To achieve the goal of neuromorphic computing hardware implementation with extremely high efficiency, low power consumption, and high density, it is necessary to develop transistor-free memristors and implement differential operation without subtraction circuits. In this study, argon ion irradiation was used during the fabrication process of a single crystalline LiNbO3 (LN) thin film to controllably introduce oxygen vacancies (OVs) into the bottom surface, which realized the modulation of OVs based on the excellent environment provided by a single-crystalline thin film. The memristive behavior of memristors was then modulated by regulating the distribution of OVs, and the effect of OVs distributed near the bottom surface of the single crystalline LN thin film on the memristive behavior was analyzed. In this way, two transistor-free memristors with opposite memristive behavior directions were fabricated. Two transistor-free memristors exhibit excellent synaptic plasticity and reliable multilevel resistance states. Based on two transistor-free memristors, a novel differential pair was constructed. Hardware implementations of direct differential operation without subtraction circuits were achieved. This study provides a new pathway to develop a transistor-free memristor and achieve differential operation without subtraction circuits in neuromorphic computing, which will simplify the peripheral circuits, improve integration density, and reduce power consumption and latency.