In general, the unit cost of inspection is assumed to be constant. However, it can be argued that the unit cost of inspection is seldom constant. In 1943, Dodge proposed the type I continuous sampling plan (CSP-1 plan) and indicated how to calculate its average outgoing quality (AOQ) and average fraction inspected (AFI). In this paper, we further propose the problem concerning the economic design of short-run CSP-1 plan under linear inspection cost. A solution procedure is developed to find the unique combination (i(superscript *), f(superscript *)) that will meet the average outgoing quality limit (AOQL) requirement, while also minimizing the total expected cost per unit produced for the short-run CSP-1 plan when the process average (average)p (AOQL) and production run length R are known. A numerical example is illustrated and the sensitivity analysis of parameters is provided.