Brake hydraulic pressure generator

First main and second hydraulic pressure paths, master cut valves configured to open and close the first and second main hydraulic pressure paths, respectively, a slave cylinder that operates in accordance with an operation amount of a brake operator, a first communication path that communicates from the slave cylinder to the first main hydraulic pressure path, and a second communication path that communicates from the slave cylinder to the second main hydraulic pressure path are provided. The slave cylinder includes a single hydraulic pressure chamber. The slave cylinder communicates with the first and second communication paths through a common flow path connected to the hydraulic pressure chamber. The slave cylinder is configured to be able to increase a pressure on a downstream side of the first or second main hydraulic pressure path. An on-off valve is provided in at least one of the first and second communication paths.