The large flange cover is one of the key components of centrifugal compressor and air separation compressor that is utilized in the aviation equipment , and the machining of the flow channel inside flange cover is a difficult problem. An electrical discharge machining method for machining an internally curved flow channel is proposed. The structure of a flexible transmission device used for EDM internal flow channel machining is studied. The bending avoidance technology, insulation & chip removal technology and EDM processing technics are prepared. Using this new method could solve the traditional mechanical processing problems, such as shorten parts service lives by drilling auxiliary holes, solve the high security risks that are caused by toxic liquid and gas leakage for easy cracking of the welding position, complex procedures and high costs. The method can achieve the high efficiency and high precision machining of the flow channel with various inclination angles. The experimental results show that this method can be used to process internal curved holes with diameter ranged from 15mm to 20mm, bending joint smooth transition and two hole docking at the accuracy of not less than 0.8 mm, surface roughness less than Ra3.2μm. This method of EDM provides an effective method for the manufacture of components with internally curved flow channel.