In this paper, we carry out a detailed study on the production of the doubly charmed baryon in deeply inelastic ep scattering (DIS) for Q2 ∈ [2, 100] GeV2, at the Large Hadron Electron Collider (LHeC) with Ee = 60(140) GeV and Ep = 7000 GeV. To exclude the contributions from the diffractive productions and the b hadron decays, we impose the kinematic cuts 0.3 < z < 0.9, and {p}_{t,mathrm{baryon}}^{star 2} > 1 GeV2 in the center-of-mass (CM) frame of γ∗p. Based on the designed LHeC luminosity, by detecting the decay channel {Xi}_{cc}^{+}left({Xi}_{cc}^{++}right)to {Lambda}_c^{+} with the subsequent decay {Lambda}_c^{+}to {pK}^{-}{pi}^{+} , we predict that about 1880 (2700) {Xi}_{cc}^{+} events and 3750 (5400) {Xi}_{cc}^{++} events can be accumulated per year, which signifies the prospect of observing them via the DIS at the forthcoming LHeC. In addition, we also predict the distributions of a rich variety of physical observables in the laboratory frame and the γ∗p CM frame, including Q2, {p}_t^2 , Y (rapidity), {p}_t^{star 2},{Y}^{star } , W, and z distributions, respectively, which can provide helpful references for studying the doubly charmed baryon. In conclusion, we think that in addition to the LHC, the LHeC is also a helpful platform for studying the properties of the doubly charmed baryon.