The time-delay control (TDC) has recently been spotlighted as an effective solution owing to model-free, efficient, and robust properties thanks to a time-delay estimation (TDE) technique. The gain of TDC, usually denoted by MN, is crucial for its stability and performance, and it is reported that the constant gain of TDC does not always guarantee the best performance. To cope with this problem, this paper proposes an effective gain adaptation together with a nonlinear desired error dynamics and a new sliding variable. The resulting adaptive gain dynamics is combined with the TDC to form the proposed control, whose closed-loop stability is proved. Through simulation and experiment, we have shown that the proposed control enables to transfer MN from an unstable initial value to a stable one, better than a best-tuned gain by trial and error. As a result, the proposed control is model-free, able to achieve time responses as fast as the inclusive enhanced TDC (IETDC) - arguably the fastest TDC - and tracking accuracy better than the IETDC. The proposed method has shown a strong potential to significantly relieve the burden of gain selection.