Fractional laser chaotic systems can exhibit more complex dynamical behavior, so its projective synchronization and applications to image encryption have been widely investigated in recent years. This work devotes to realize its function matrix projective synchronization, whose projective scale factor is a function matrix varying with time t, and applies the function matrix projective synchronization to the color image encryption. First, two different fractional laser chaotic systems with model uncertainty and external disturbance are constructed and the function matrix projective synchronization is defined. Second, the fractional sliding mode surface and the sliding mode controller are designed to achieve the function matrix projective synchronization. And, the synchronization analysis is confirmed by numerical simulation. Finally, by Zigzag transformation and DNA coding, the function matrix projective synchronization is applied to the color image encryption. And the comparison results shows that an excellent encryption scheme can be designed by the complex projection factor. This work not only extends the concept of the projective synchronization, but also provides an effective method for the image encryption.