Results are presented of an X-ray investigation of several Crab-like supernova remnants (SNRs), especially those with central pulsars. A statistical relationsip was obtained between the total X-ray luminosity of an isolated pulsar and its nebula in the 0.2-4.0 keV band and the rotating energy loss rate of the pulsar. The relationship strongly suggests that the energy source of X-rays both from an isolated pulsar and its nebula comes from the rotating energy loss of the pulsar, and that the energy transformation may be simple and direct. Data obtained on the surface brightness of a Crab-like SNR with a central compact source but with no pulsating signals, such as the 3C 58 SNR, show that the central part of this SNR coincides with that of a point source calibration. Reasons are suggested for the observation that some compact sources in Crab-like SNRs might not appear as pulsars.