A bicycle hub gearbox is provided for a multi-speed hub with a coaster brake mechanism. The bicycle hub gearbox basically has a first planetary gear mechanism, a second planetary gear mechanism, a braking mechanism and a clutch mechanism. The second planetary gear mechanism is operatively coupled with the first planetary gear mechanism. The braking mechanism is selectively coupled to the first planetary gear mechanism. The clutch mechanism selectively couples an output side of the first planetary gear mechanism to an input side of the second planetary gear mechanism to selectively transmit either a driving torque applied by a rider in a driving direction depending on a selected gear ratio or a braking torque applied by the rider in a braking direction to the braking mechanism independent of a selected gear ratio via one path such that a resulting braking effect is substantially equal independent of the selected gear ratio.