This study proposes a novel stair-climbing wheelchair based on lever propulsion control using the human upper body. Wheelchairs are widely used as supporting locomotion devices for people with acquired lower limb disabilities. However, steps and stairs are critical obstacles to locomotion, which restrict their activities when using wheelchairs. Previous research focused on power-assisted, stair-climbing wheelchairs, which were large and heavy due to its large actuators and mechanisms. In the previous research, we proposed a wheelchair with lever propulsion mechanism and presented its feasibility of climbing up the stairs. The developed stair-climbing wheelchair consists of manual wheels with casters for planar locomotion and a rotary-leg mechanism based on lever propulsion that is capable of climbing up stairs. The wheelchair also has a passive mechanism powered by gas springs for posture transition to shift the user's center of gravity between the desired positions for planar locomotion and stair-climbing. In this paper, we present an advanced study on both climbing up and going down using lever propulsion control by the user's upper body motion. For climbing down the stairs, we reassembled one-way clutches used for the rotary-leg mechanism to help a user climb down the stairs through lever operation. We also equipped the wheelchair with sufficient torque dampers. The frontal wheels were fixed while climbing down the stairs to ensure safety. Relevant experiments were then performed to investigate its performance and verify that the wheelchair users can operate the proposed lever propulsion mechanism.