The production of isolated photons in deep-inelastic scattering ep→eγX is measured with the H1 detector at HERA. The measurement is performed in the kinematic range of negative four-momentum transfer squared 4<Q2<150 GeV2 and a mass of the hadronic system WX>50 GeV. The analysis is based on a total integrated luminosity of 227 pb-1. The production cross section of isolated photons with a transverse energy in the range 3<ET γ<10 GeV and pseudorapidity range -1.2<ηγ<1.8 is measured as a function of ET γ, ηγ and Q2. Isolated photon cross sections are also measured for events with no jets or at least one hadronic jet. The measurements are compared with predictions from Monte Carlo generators modelling the photon radiation from the quark and the electron lines, as well as with calculations at leading and next to leading order in the strong coupling. The predictions significantly underestimate the measured cross sections.