“TSUBAME” is a university-built small satellite mission to measure polarization of hard X-ray photons (30-200 keV) from gamma-ray bursts (GRBs) using azimuthal anisotropy of Compton-scattered photons. Polarimetry in the hard X-ray and soft γ-ray bands should provide crucial information for understanding the high-energy emission mechanisms and the distribution of magnetic fields and radiation fields in the astrophysical sources. TSUBAME has two instruments: the Wide-field Burst Monitor (WBM) and the Hard X-ray Compton Polarimeter (HXCP). The WBM determines on board the direction of the burst occurrence with an accuracy of 10 degrees, then using a high speed attitude control device, the HXCP is pointed to the GRB within 15 seconds after the burst occurrence to promptly detect polarized X-ray photons from the GRB. We present an overview of the TSUBAME mission, its estimated scientific capability for detecting GRBs and measuring their X-ray polarization, development of multi-anode photomultiplier tubes that use ultra bi-alkali photocathodes, and the future plans of this mission.