We investigate the power spectra of the CMB temperature and matter density in the running vacuum model ( RVM ) with the time-dependent cosmological constant of \Lambda = 3 \nu H ^ { 2 } + \Lambda _ { 0 } , where H is the Hubble parameter . In this model , dark energy decreases in time and decays to both matter and radiation . By using the Markov chain Monte Carlo method , we constrain the model parameter \nu as well as the cosmological observables . Explicitly , we obtain \nu \leq 1.54 \times 10 ^ { -4 } ( 68 % confidence level ) in the RVM with the best-fit \chi ^ { 2 } _ { \mathrm { RVM } } = 13968.8 , which is slightly smaller than \chi ^ { 2 } _ { \Lambda \mathrm { CDM } } = 13969.8 in the \Lambda CDM model of \nu = 0 .