Spontaneous imbibition of the injected fluid into the pore space of a tight oil reservoir and replacing the crude oil therein has been considered as one of the possible mechanisms in increasing oil recovery. Such deeply buried reservoir rocks is usually under high-pressure and high-temperature conditions. Besides, their interior complex porous structures are usually characterized as pore bodies and slit-shaped pore throats. As a result, an accurate description of the spontaneous imbibition behavior driven by capillary force in the real pore space under reservoir conditions is crucial to understand the process and uncover the controlling mechanisms. An improved multi-component pseudo-potential lattice Boltzmann method was developed to simulate the spontaneous imbibition behavior in a representative 3D pore space extracted from a tight sandstone reservoir rock. Comparison of the spontaneous imbibition behavior under ambient condition and reservoir condition showed that the latter case exhibited two times faster of the imbibition. Moreover, a snap-off of the oil droplet phenomenon was observed in the pore bodies surrounded by slit-shaped pore throats. The snap-off oil droplets stuck in the pore bodies and accounted for 9.47 % of the pore volume. These results indicated the importance of investigating the spontaneous imbibition in a real porous structure and under actual reservoir condition. The proposed pore-scale simulation method provides a useful tool in understanding the complex spontaneous imbibition pattern and the resulted enhanced oil recovery.