We have collected almost all HdC, RCB and EHe stars up to date to investigate their infrared properties, in particular, their radiation mechanisms in the infrared, using the observational data from 2MASS, WISE and IRAS missions. Because HdC stars, RCB stars and EHe stars all belong to the category of extremely hydrogen deficient stars and they definitely have some evolutionary connections. It is found from this paper that all RCB stars have infrared excesse in the wavelength region from the near infrared to the far infrared covered by 2MASS, WISE and IRAS due to dust while almost all HdC stars and EHe stars have no or little infrared excess. From 2MASS, WISE and IRAS two-color diagrams, it is also found that the majority of these three kinds of stars are around the power law distributions in the near infrared possibly indicative of their infrared radiations from the warm dust in the disk-like envelope. It is also found that in the mid-and far infrared regions some stars are around the power law distribution perhaps due to dust from disk-like envelope while some stars are around the blackbody distribution maybe due to the cold and extended nebulosity nearby.