In order to study further the long-range correlations ("ridge") observed recently in p+Pb collisions at sNN=5.02TeV, the second-order azimuthal anisotropy parameter of charged particles, v2, has been measured with the cumulant method using the ATLAS detector at the LHC. In a data sample corresponding to an integrated luminosity of approximately 1μb−1, the parameter v2 has been obtained using two- and four-particle cumulants over the pseudorapidity range |η|<2.5. The results are presented as a function of transverse momentum and the event activity, defined in terms of the transverse energy summed over 3.1<η<4.9 in the direction of the Pb beam. They show features characteristic of collective anisotropic flow, similar to that observed in Pb+Pb collisions. A comparison is made to results obtained using two-particle correlation methods, and to predictions from hydrodynamic models of p+Pb collisions. Despite the small transverse spatial extent of the p+Pb collision system, the large magnitude of v2 and its similarity to hydrodynamic predictions provide additional evidence for the importance of final-state effects in p+Pb reactions.