Abstract: A generalized P-value, namey the bounded P-value, is defined and studied in this paper. It is known that for the one sided testing problem of the normal mean H₀:θ≤θ₀, the P-value is the probability of the rejection region under θ=θ₀. Based on this consideration a bounded P-value is defined for general case, in which the null hypothesis is determined by a closed convex cone. Some properties of the bounded P-value are discussed and a numerical example is analized by using the results.