We will upgrade atmospheirc neutrino flux calculation by M. Honda (Honda flux), which has been used as a flux prediction in many experiments including Super-Kamiokande and has greatly contributed in the neutrino physics. The dominant uncertainty of the Honda flux arises from insufficient understanding of the hadron interactions inside air showers. Conventionally hadron interaction model in Honda flux has been tuned based on atmospheric muon observation data, but it arises relatively large uncertainties in momentum region below 1 GeV/$c$ and above $O(10)$ GeV/$c$. Recently several precise measurements for hadron production using accelerator beams have been performed. We incorporate the accelerator-data-driven tuning into Honda flux calculation to complement the muon tuning.