Low-energy electron diffraction (LEED) and Auger electron spectroscopy (AES) were used to study the initial growth of a cobalt ultrathin film on a Pt(111) surface. The growth of the cobalt ultrathin film on Pt(111) belongs to Stranski-Krastanov mode. The kinetics of the inter-diffusion of Co adatoms on a Pt(111) surface was studied by AES at various temperatures with the Co coverage of one monolayer. The activation energy and the pre-exponential diffusion coefficient are obtained to be 0.90 eV and 6.6 x 10^(-11) cm^2/s respectively from an Arrhenius plot. Ultraviolet photoelectron spectroscopy (UPS) was used to monitor the alloy formation of Co/Pt(111) in the annealing process.