A compact Drift-Tube-Linac (DTL) using an Interdigital H-mode (IH) cavity was designed for an injector of medical accelerators. For beam focusing, the method of Alternating-Phase-Focusing (APF) was applied. The APF IH-DTL can accelerate heavy ions having acharge-to-mass ratio of q=m . 1 3 up to 4:0MeV=u. Having optimized an array of synchronous phases for cells, namely arranging drift tubes and gaps appropriately, both longitudinal and transverse focusing strengths were produced just with the rf acceleration field, and therefore no focusing element or cooling equipments had to be installed in the cavity. This allowed us to employ a rather high operating frequency, and hence to design a compact and cost-effective cavity. A further advantage ...