This paper calculates quantum-mechanically the photoelectron energy spectra excited by attosecond x-rays in the presence of a few-cycle laser. A photoelectron laser phase determination method is used for precise measurements of the pulse natural properties of x-ray intensity and the instantaneous frequency profiles. As a direct procedure without any previous pulse profile assumptions and time-resolved measurements as well as data fitting analysis, this method can be used to improve the time resolutions of attosecond timing and measurements with metrological precision. The measurement range is half of a laser optical cycle.