Reliability demonstration tests with zero-failure acceptance criterion are most commonly used in the field of reliability application since they require fewer test samples and less test time compared to other test methods that guarantee the same reliability with a given confidence level. For products with lognormal lifetime distribution, an economic zero-failure test plan is developed that minimizes the total cost related to perform a life test to guarantee a specified reliability of a product with a given confidence level. A numerical example is provided to illustrate the use of the proposed test plan.