NEWAGE is a direction-sensitive dark matter search experiment using a micro-time-projection chamber filled with CF4 gas. Following our first underground measurement at Kamioka in 2008, we developed a new detector with improved sensitivity, NEWAGE-0.3b'. NEWAGE-0.3b' has twice the target volume of the previous detector, a lower energy threshold, and an improved data acquisition system. In 2013, a dark matter search was undertaken by NEWAGE-0.3b' in Kamioka underground laboratory. The exposure of 0.327 kg • days achieved a new 90% confidence level direction-sensitive spin-dependent cross-section limit of 557 pb for a 200 GeV/c2 weakly interacting massive particle. Relative to our first underground measurements, the new direction-sensitive limits are improved by a factor of ~ 10, and are the best achieved to date.