Abstract: Electron with an appropriate initial velocity injected into an oncoming, ultra-intense circularly polarized laser pulse will execute circular relativistic motion at the peak of laser pulse. The circulating electron then radiates in the same manner as that in the storage ring of a conventional synchrotron source. Owing to the extremely small orbit radius, the laser-field synchrotron radiation thus generated is an attosecond or zeptosecond X-ray pulse. The pulse width of the scattered radiation decreases and the power of the scattered radiation increases with increasing the intensity of the laser pulse and the electron’s initial energy. The unique feature makes the laser-field synchrotron radiation a promising synchrotron radiation source with short wavelength and short duration.