We present the first LHAASO catalog of γ-ray sources with energies above 25 TeV. The catalog covers the northern γ-ray sky from declination $-20^{\circ}$ to $80^{\circ}$, and it is based on data collected by the LHAASO 1 km$^2$ array (LHAASO-KM2A) from January 2020 to September 2022. It represents the most sensitive survey of these sources in this energy range, including 75 detections with a confidence level above 5σ and an extended size of less than $2^\circ$. Among them, 43 sources have been detected with ultra-high energy ($>$100 TeV) emissions with a significance level higher than 4σ (TS > 25). The position, extension and power-law spectral characteristics of each source are reported.