Frequency drop due to loss of massive generation is a threat to power system frequency stability. Under-frequency load shedding (UFLS) is the principal measure to prevent successive frequency declination and blackouts. Based on traditional stage-by-stage UFLS scheme, a new continuous UFLS scheme is proposed in this paper to shed loads proportional to frequency deviation. The characteristic of the proposed scheme is analyzed with a closed-form solution of frequency dynamics. Frequency threshold and time delay are added to make the proposed scheme practical. A line-by-line scheme based on precise load control is introduced to implement the continuous scheme for systems without enough continuously controllable loads. The load shedding scale factor of the proposed scheme is tuned with an analytical method to achieve adaptability to different operating conditions. The adaptability of the proposed scheme is validated with 39-bus New England model and simplified Shandong Power Grid of China.