Electromagnetic form factors, which parametrize the inner structure of hadrons, are fundamental observables for understanding the strong interaction. The electron-positron collider experiments are powerful tools to study the electromagnetic form factors of various baryons in time-like region via energy scan or ISR-return methods. In this contribution， we report on the recent measurements of baryon electromagnetic form factors at the BESIII experiment. Taking advantage of large statistics, the moduli of the electric and magnetic form factors of $n$ are measured separately for the first time at center-of-mass energy from 2.00-2.95~GeV. Moreover, new results about the hyperon ($\Lambda$, $\Sigma$, $\Lambda_{c}$, $\Delta$, $\Omega$) pair production cross section and form factors are presented. The anomalous threshold effect is observed in some pair production channels and an oscillation behavior is observed, for the first time, in the energy dependence of the ratio between modulus of the electric and magnetic form factor for $\Lambda_{c}$ baryon. In addition, a complete measurement of $\Sigma^{+}$ form factors is achieved in a wide $q^{2}$ region.