Fast radio bursts (FRBs) are mysterious millisecond pulses in radio, most of which originate from distant galaxies. Revealing the origin of FRBs is becoming central in astronomy. The redshift evolution of the FRB energy function, i.e. the number density of FRB sources as a function of energy, provides important implications for the FRB progenitors. Here, we show the energy functions of FRBs selected from the recently released Canadian Hydrogen Intensity Mapping Experiment (CHIME) catalogue using the V_max_ method. The V_max_ method allows us to measure the redshift evolution of the energy functions as it is without any prior assumption on the evolution. We use a homogeneous sample of 164 non- repeating FRB sources, which are about one order of magnitude larger than previously investigated samples. The energy functions of non-repeating FRBs show Schechter function-like shapes at z <~ 1. The energy functions and volumetric rates of non-repeating FRBs decrease towards higher redshifts similar to the cosmic stellar-mass density evolution: there is no significant difference between the non-repeating FRB rate and cosmic stellar-mass density evolution with a 1 per cent significance threshold, whereas the cosmic star-formation rate scenario is rejected with a more than 99 per cent confidence level. Our results indicate that the event rate of non-repeating FRBs is likely controlled by old populations rather than young populations that are traced by the cosmic star- formation rate density. This suggests old populations, such as old neutron stars and black holes, as more likely progenitors of non-repeating FRBs.