Due to the small ohmic resistance, such as the LFP battery, off-line state-of-health (SOH) estimation based on ohmic techniques faces a great challenge on measurement difficulty. The inaccurate measurement result of the ohmic resistance can cause a severe SOH error. This paper studies the influences of battery external resistance on the off-line SOH estimations using different model parameters in a first-order equivalent battery model. The sensitivity function is introduced here to assess performances of these model parameters. The several test results show that the transient resistance has the good ability against the external resistance effect. The sensitivity results of the transient resistance are all less 0.05 in different test cases. In addition, the SOHs estimated by the transient resistance and full charge capacity (FCC) in 600 cycling tests have the smallest average error (6.9%).