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A photonic microwave true-time delay using a tapered chirped fibre Bragg grating is proposed and fabricated. A resistive heating electrode coated on the tapered fibre and a single-wavelength light was incorporated to control the time delay continuously without any mechanical perturbation and moving. It was achieved by adjusting the reflection positions of the optical signal carrying the microwave signal from within the tapered grating via the thermo-optic effect. The measured time delay was ∼120 ps with electrical power consumption of 250 mW.