This paper proposes an adaptive single-carrier modulation with frequency domain equalization (SC-FDE) scheme further enhancing frequency diversity benefit. We have so far proposed the periodic spectrum transmission realized by the even-numbered time domain samples, which further improves the bit error rate (BER) of SC-FDE in severe frequency selective fading channels. However, in frequency non-selective fading channels, the periodic spectrum transmission provides worse BER than the traditional non-periodic transmission. Therefore, the proposed adaptive transmission chooses the appropriate transmission mode by comparing the error vector magnitudes (EVM) of the periodic and non-periodic transmissions. Moreover, since the EVM is measured by the CAZAC-based pilot signals used for channel estimation, additional redundancy is not needed any more. Numerical results show that the proposed adaptive scheme always provides the best performance irrespective of the frequency selectivity in channels while its frequency selectivity gives some BER degradation in the periodic and non-periodic transmissions.