The human circulatory system comprises a complex network of blood vessels interconnecting biologically relevant organs and a heart driving blood recirculation throughout this system. Recreating this system in vitro would act as a bridge between organ-on-a-chip and "body-on-a-chip" and advance the development of in vitro models. Here, we present a microfluidic circulatory system integrated with an on-chip pressure sensor to closely mimic human systemic circulation in vitro. A cardiac-like on-chip pumping system is incorporated in the device. It consists of four pumping units and passive check valves, which mimic the four heart chambers and heart valves, respectively. Each pumping unit is independently controlled with adjustable pressure and pump rate, enabling users to control the mimicked blood pressure and heartbeat rate within the device. A check valve is located downstream of each pumping unit to prevent backward leakage. Pulsatile and unidirectional flow can be generated to recirculate within the device by programming the four pumping units. We also report an on-chip capillary-assisted pressure sensor to monitor the pressure inside the device. One end of the capillary was placed in the measurement region, while the other end was sealed. Time-dependent pressure changes were measured by recording the movement of the liquid-gas interface in the capillary and calculating the pressure using the ideal gas law. The sensor covered the physiologically relevant blood pressure range found in humans (0-142.5 mmHg) and could respond to 0.2 s actuation time. With the aid of the sensor, the pressure inside the device could be adjusted to the desired range. As a proof of concept, human normal left ventricular and arterial pressure profiles were mimicked inside this device. Human umbilical vein endothelial cells (HUVECs) were cultured on chip and cells can respond to mechanical forces generated by arterial-like flow patterns.