Abstract: From the point of view of the principle of special relativity, it can be known that under the Lorentz transformation of space and time, the electromagnetic field vectors are different with the inertial frames, but the forms of the Maxwell equations are invariant. According to Faraday's law of electromagnetic induction and Ampere's law based on Maxwell's hypothesis of displacement current, the expressions for relativity of time-varying electromagnetic field in resourceless free space to inertial frames which move relatively in low speed are derived concisely. In addition, the form invariance of the basic equations of time-varying electromagnetic field based on the obtained expressions is discussed. The gained results are very important to help ones understand and apply Maxwell's equations of time-varying electromagnetic field.