The observation of very high energy (VHE,> 100GeV) photon from γ-ray bursts (GRBs) can advance our understanding of their radiation mechanism, the evolution of host-galaxies, violations of Lorentz invariance, extragalactic background light, and intergalactic magnetic field. Recently the measurements on VHE emission from afterglow phase have blossomed and borne fruit while detection of the prompt emission is rare. It is important to observe prompt emissions by ground-based instruments which take advantage of wide field of view and high duty cycle. Up to now, GRB 190829A is the nearest GRB with VHE afterglow emissions. The detection of its VHE emission was announced by H.E.S.S. at about 4h 20m after the burst. While during its prompt phase, GRB 190829A was at the edge of the field of view of LHAASO. Benefiting by the high altitude of 4410 m and the triggerless observation mode, the energy threshold of LHAASO is largely reduced to tens of GeV. This work presents the search for VHE γ-ray emission from GRB 190829A with the triggerless data taken by the first pond of LHAASO-WCDA. The analysis shows no indication of VHE emission neither in the prompt nor in the first 2 hours of afterglow phase, thus 95% upper limits are yielded. Furthermore, the upper limits of prompt phase was used to constrain the spectral parameter space of VHE extra component based on a phenomenological model