Envelope tracking (ET) technology provides the potential for achieving high efficiency in power amplifiers (PAs) with high peak-to-average ratio (PAR) signals. Envelope amplifiers with high fidelity, high efficiency, and wide bandwidth are critical components for the widespread application of envelope tracking. This paper presents the design of a linear-assisted switching buck converter for use in an envelope amplifier. To effectively leverage the high efficiency of buck converters and the wide bandwidth capabilities of linear amplifiers, a parallel combination of these two devices is employed in this work. A novel current-sense constant-on-time (COT) controller is proposed to coordinate this hybrid power supply. The combination mainly enables the switching converter to provide the average power required by the PA with high efficiency, while the wideband linear amplifier provides a wide range of dynamic voltages. The technique improves the efficiency of the envelope amplifier, especially for applications requiring high PAR with wider bandwidth signals. Measurement of the envelope amplifier showed an efficiency of approximately 77% with 10 W output power using LTE downlink signals. The overall ET system was demonstrated by using a GaN PA. The measured average power-added efficiency of the amplifier reached above 45% for an LTE modulated signal with 20 MHz bandwidth and PAR of 8.0 dB, at an average output power of 5 W and gain of 10.1 dB. The measured normalized RMS error is below 2.1% with adjacent channel leakage ratio of -48 dBc at an offset frequency of 20 MHz.