We performed and studied cascaded third-harmonic generation (THG) in a quasi-periodically poled KTP (QPPKTP) crystal allowing simultaneous phase-matching of the two cascading steps ω + ω → 2ω and 2ω + ω → 3ω. The phase-matching was achieved at the fundamental wavelength λω = 1587 nm when the QPPKTP crystal was heated to 95°C. The energy conversion efficiency reached 40% in the picosecond regime for a fundamental energy of 20 µJ that corresponds to an intensity of 1.5 GW/cm2. It is the highest value of THG efficiency ever reported to the best of our knowledge. The modeling in the case of the depleted pump regime accurately described the experiments.