We present a compact electro-absorption slow-light modulator laterally-integrated with a 980-nm VCSEL. We figured out the small signal modulation response for different modulator lengths. While the 3-dB small-signal modulation bandwidth of conventional directly modulated VCSELs on the same epi-wafer structure was limited below 10 GHz, we obtained a modulation bandwidth over 21 GHz for a 30 µm long modulator. We also demonstrated large signal modulation up to 25 Gbps with a low driving voltage below 600 mV(pp) and an extinction ratio of 4 dB for the modulator length of 50 µm. Prospects of much higher speed (> 40 Gbps) were examined with reducing the size of the modulator. Also, the tapered waveguide coupling structure enables "quasi-unidirectional coupling", which reduces the optical feedback in a VCSEL from the integrated modulator.