Double Hopf bifurcation of codimension 2 singularity in a type of two cells oscillator with interaction feedback connection is investigated. With the introduction of time delay which represents the communication time between cells, the stability switching phenomena is observed and double Hopf bifurcation occurs at the intersection point of Hopf lines. The geometrical scheme is applied in analyzing system stability underlying multiple time delays. The numerical simulation discovers that either the vicinity of bifurcating periodical solution on the margin of Hopf lines or the coexistence phenomena of five periodical solutions induced by stability switching phenomena. By applying the Schmidt dimensional reduction technique combined with the center manifold theory, the normal form of double Hopf point is calculated by parameter perturbation method and the near dynamics of double Hopf point is classified. The bifurcating periodical solutions and quasi-periodical solutions are observed which are in consistence with the numerical simulation results.