The famed yet elusive H-dibaryon, an exotic quark state (uuddss), was predicted several decades ago and also supported by recent Lattice QCD calculations. The E42 experiment has been approved at J-PARC to search for the H-dibaryon with high statistics. A large acceptance hyperon spectrometer with a time projection chamber (TPC) will be used for searching the H-dibaryon from (K − , K + ) reaction off nuclei via its possible following decays such as ΛΛ. The E42 experiment has high sensitivity both above and below ΛΛ threshold and will be the definitive experiment on the existence of the H-dibaryon, once and for all. Recent progress and achievements of the E42 collaboration will be presented, which include simulations on estimation of TPC performance in the electric field and the magnetic field, testing and optimization of a prototype TPC, and preparation of various detectors.