In this paper we present astrophysical parameters of the very old open star cluster Berkeley 39 using 2MASS JHK data and observation of BV CCD photometry (V ~ 21.5 mag) in Johnson-Cousin filters. We have derived reddening, distance, metallicity and age etc. using two color diagrams in near-infrared and optical bands. We have found EB-V = 0.099 ± 0.02, EJ-H = 0.018 ± 0.001 and EJ-Ks = 0.016 ± 0.001 mag, and the distance modulus of (m-M) 0 = 13.24 ± 0.03 mag, which give a distance of 4.2 ± 0.04 Kpc, and the age of the cluster is 5.6 Gyr with metallicity; Z = 0.008 (obtained from fitting of the observed CMDs with Padova iso-chrones). The radius of the cluster obtained from the analysis of 2MASS data is equal 9.0 ± 0.13 arc minutes; it reflects that the cluster have large radius with new cluster center. Luminosity and mass functions have been investigated as well as the dynamical relaxation time of the cluster Berkeley 39.