The pseudorapidity density of charged particles (\(\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\)) at mid-rapidity in Pb-Pb collisions has been measured at a center-of-mass energy per nucleon pair of \(\sqrt{s_{\rm NN}}\) = 5.02 TeV. It increases with centrality and reaches a value of \(1943 \pm 54\) in \(|\eta|<0.5\) for the 5% most central collisions. A rise in \(\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\) as a function of \(\sqrt{s_{\rm NN}}\) for the most central collisions is observed, steeper than that observed in proton-proton collisions and following the trend established by measurements at lower energy. The centrality dependence of \(\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\) as a function of the average number of participant nucleons, \({\langle N_\mathrm{part} \rangle}\), calculated in a Glauber model, is compared with the previous measurement at lower energy. A constant factor of about 1.2 describes the increase in \(\frac{2}{\langle N_\mathrm{part} \rangle}\langle \mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta \rangle\) from \(\sqrt{s_{\rm NN}}\) = 2.76 TeV to \(\sqrt{s_{\rm NN}}\) = 5.02 TeV for all centrality intervals, within the measured range of 0-80% centrality. The results are also compared to models based on different mechanisms for particle production in nuclear collisions.