Using 2917pb -1 of data accumulated at 3.773GeV, 44.5pb -1 of data accumulated at 3.65GeV and data accumulated during a ψ(3770) line-shape scan with the BESIII detector, the reaction e+e-→pp- is studied considering a possible interference between resonant and continuum amplitudes. The cross section of e+e-→ψ(3770)→pp-, σ(e+e-→ψ(3770)→pp-), is found to have two solutions, determined to be (0.059-0.020+0.070±0.012)pb with the phase angle φ=(255.8-26.6+39.0±4.8)° (<0.166pb at the 90% confidence level), or σ(e+e-→ψ(3770)→pp-)=(2.57-0.13+0.12±0.12)pb with φ=(266.9-6.3+6.1±0.9)° both of which agree with a destructive interference. Using the obtained cross section of ψ(3770)→pp-, the cross section of pp-→ψ(3770), which is useful information for the future PANDA experiment, is estimated to be either (9.8-3.9+11.8)nb (<27.5nb at 90% C.L.) or (425.6-43.7+42.9)nb. © 2014 Elsevier B.V.