Similarly to but quite different from the xenon poisoning effects resulting from fission-produced iodine during the restart-up process of a fission reactor, we introduce a completely new concept of the tritium bu-up depth and tritium break-even time in the fusion energy research area. To show what the least required amount of tritium storage is used to start up a fusion reactor and how long a time the fusion reactor needs to be operated for achieving the tritium break-even during the initial start-up phase due to the finite tritium breeding time that is dependent on the tritium breeder, specific structure of breeding zone, layout of coolant flow pipe, tritium recovery scheme, extraction process, the tritium retention of reactor components, unrecoverable tritium fraction in breeder, leakage to the inertial gas container, and the natural decay etc., we describe this new phenomenon and answer this problem by setting up and by solving a set of equations, which express a dynamic subsystem model of the tritium inventory evolution in a fusion experimental breeder (FEB). It is found that the tritium bu-up depth is 317g and the tritium break-even time is approximately 240 full power days for FEB designed detail configuration and it is also found that after one-year operation, the tritium storage reaches 1.18kg that is more than theleast required amount of tritium storage to start up three of FEB-like fusion reactors.