A Superstructure Grating(SSG) Distributed-Bragg-Reflector(DBR) laser has a broad tuning range with a good mode suppression ratio. However, gaps of channel are observed in the wavelength-tuning characteristics of an SSGDBR laser which employs linearly-chirped DBR mirrors. We found by numerical simulation that the gaps may be attributed to the nonuniform reflection-peak heights of a linearly-chirped DBR mirrors. We propose a nonlinearly chirped grating DBR mirror structure that makes reflection-peak heights almost uniform. Therefore a nonlinearly chirped grating structure can be employed in an extended tuning range semiconductor laser to achieve gap-free tuning and low threshold current operation simultaneously.