Data and code for the paper "Parameter estimation for ocean background vertical diffusivity coefficients in the Community Earth System Model (v1.2.1) and its impact on ENSO forecast" includes: The model is Community Earth System Model (v1.2.1) (provided by www.cesm.ucar.edu) Data assimilation code is initially provided by Data Assimilation Research Testbed (DART) (https://dart.ucar.edu/), some modifications are made to enable parameter estimation function of ocean background vertical diffusivity coefficients. And the programs and scripts for deal with OISST and EN4 profiles are also developed. The parameter sensitivity experiment results are saved as sensitive2008-2012.nc and sensitive2008-2012salt.nc for temperature and salinity, respectively. And the python script to draw the results is The state estimation results are provided as Temp_05-17.nc and Salt_05-17.nc for temperature and salinity, respectively. The parameter estimation results are provided as PE_Temp_05-17.nc and PE_Salt_05-17.nc for temperature and salinity, respectively. the estimated paremeter ensemble is saved in parameters.nc the python script for comparing the SE and PE results is plot_analysis.py the nino3.4 indices computed by the forecast experiment is saved in fcst_correlation.nc