Abstract In this paper, the class of weakly ω-admissible paratopological groups is introduced. We mainly show that: (1) Every bounded set in a weakly ω-admissible paratopological group is p-bounded for each free ultrafilter p on ω; (2) every C-compact set in a weakly ω-admissible paratopological group is strongly r-pseudocompact. The class of weakly ω-admissible paratopological groups contains all totally ω-narrow, precompact, locally feebly compact, weakly Lindelof and saturated, and ω-admissible paratopological groups. It is worth mentioning that all the aforementioned spaces are not to satisfy any separation axiom. Some Sanchis, Sanchez and Tkachenko's results are improved.