An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for 2D wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension $D$. We show that for the doped Hubbard model in the strongly correlated regime ($U/t=8$, $n=0.875$) iPEPS yields lower variational energies than state-of-the-art variational methods in the large 2D limit, which demonstrates the competitiveness of the method. In order to obtain an accurate estimate of the energy in the exact infinite $D$ limit we introduce and test an extrapolation technique based on a truncation error computed in the iPEPS imaginary time evolution algorithm. The extrapolated energies are compared with accurate quantum Monte Carlo results at half filling and with various other methods in the doped, strongly correlated regime.
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