The present invention provides a process for continuous treatment of high-concentration organic wastewater and a device for continuous treatment of high-concentration organic wastewater. The process of the present application is that: high-concentration organic wastewater is continuously separated through the synergistic interaction of a multilayer evaporator and a heat pump, and the generated wastewater steam containing light components is continuously subjected to desulfurization and catalytic combustion after being mixed with air in a gaseous form, the treated wastewater can meet discharge standards, and heavy components of the generated wastewater can be recycled. After the desulfurizing agent in a first desulfurizer and the catalyst in a first catalytic combustor are deactivated, the generated wastewater steam containing the light components can be switched to a second desulfurizer and a second catalytic combustor for reaction, and air can be introduced into the deactivated catalyst and desulfurizing agent for in-situ regeneration at a high temperature.