Additive manufacturing of lightweight and energy-efficient composite using continuous fibers to reinforce thermoset polymers is highly desirable. However, the material, architectural, and technical limitations make existing AM technologies unavailable for printing structural and functional thermoset/continuous carbon fiber composite. In our work, we overcome these difficulties and introduced a new AM technology by creating a controllable resin system and a dynamic curing window to enable fast solidification of composite to hold the shape, realizing a feasible 3D printing of thermoset/continuous carbon fiber composite with near net shape, complex geometry, and programmable performance. Our process enables us to print composite with overhanding structure in free space, without need for support material. This AM technology provides a new 3D printing concept and process knowledge beyond existing AM technologies to potentially enable high throughput processing and geometric complexity of printed composite, and could promisingly produce a transformative impact on the upgrade of additive manufacturing.