For MeV gamma-ray astronomy, we have developed an electron-tracking Compton camera (ETCC) as a MeV gamma-ray telescope capable of rejecting the radiation background and attaining the high sensitivity of near 1 mCrab in space. Our ETCC comprises a gaseous time-projection chamber (TPC) with a micro pattern gas detector for tracking recoil electrons and a position-sensitive scintillation camera for detecting scattered gamma rays. After the success of a first balloon experiment in 2006 with a small ETCC (using a 10$times$10$times$15 cm$^3$ TPC) for measuring diffuse cosmic and atmospheric sub-MeV gamma rays (Sub-MeV gamma-ray Imaging Loaded-on-balloon Experiment I; SMILE-I), a (30 cm)$^{3}$ medium-sized ETCC was developed to measure MeV gamma-ray spectra from celestial sources, such as the Crab Nebula, with single-day balloon flights (SMILE-II). To achieve this goal, a 100-times-larger detection area compared with that of SMILE-I is required without changing the weight or power consumption of the detector system. In addition, the event rate is also expected to dramatically increase during observation. Here, we describe both the concept and the performance of the new data-acquisition system with this (30 cm)$^{3}$ ETCC to manage 100 times more data while satisfying the severe restrictions regarding the weight and power consumption imposed by a balloon-borne observation. In particular, to improve the detection efficiency of the fine tracks in the TPC from $sim$10% to $sim$100%, we introduce a new data-handling algorithm in the TPC. Therefore, for efficient management of such large amounts of data, we developed a data-acquisition system with parallel data flow.