Abstract: By introducing random mapping and truth degree weight function,we define the varialble randomized truth degree of formula in R0-type 4-valued non-totally ordered propositional logic system.The basic properties of variable randomized truth degree are obtained in this paper.The concept of randomized similarity and randomized pseudo-metric is introduced and randomized logic metric space in R0-type 4-valued non-totally ordered propositional logic system is also established,which provides possible framework for approximate reasoning in the logic system of 4-valued non-totally ordered propositional logic system.