Time-dependent dielectric breakdown (TDDB), which is used to measure reliability, depends on both the thickness of the tunnel barrier and bias voltage. In addition, the heat generated by self-heating in a magnetic tunneling junction (MTJ) affects TDDB. Therefore, we investigated TDDB with the self-heating effect for a MgO tunnel barrier with thicknesses of 1.1 and 1.2 nm by the constant voltage stress (CVS) method. Using the results of this experiment, we predicted a TDDB of 1.0 nm for the tunnel barrier. Also, we suggested the use of not only the CVS method, which is a common way of determining TDDB, but also the constant current stress (CCS) method, which compensates for the disadvantages of the CVS method.