The charged-particle pseudorapidity density measured over four units of pseudorapidity in nonsingle-diffractive p+Pb collisions at a center-of-mass energy per nucleon pair sqrt(s_NN)=5.02  TeV is presented. The average value at midrapidity is measured to be 16.81±0.71  (syst), which corresponds to 2.14±0.17  (syst) per participating nucleon, calculated with the Glauber model. This is 16% lower than in nonsingle-diffractive pp collisions interpolated to the same collision energy and 84% higher than in d+Au collisions at sqrt(s_NN)=0.2  TeV. The measured pseudorapidity density in p+Pb collisions is compared to model predictions and provides new constraints on the description of particle production in high-energy nuclear collisions.