An experimental method of measuring the secondary neutron angular spectrum from polyethylene slab assembly with D-T neutron source based on the proton-recoil method is developed. In order to ensure the energy linearity of the detector and obtain a good neutron-gamma discrimination capability in the case of a low effective neutron threshold (0.5MeV), neutron energy spectrum is measured in two parts: one is in a high energy region and the other in a lower energy region. The pulse shape discrimination (PSD) and the pulse height distribution (PH) two-dimensional information of the secondary neutron and the associated gamma rays are recorded event-by-event simultaneously. The selection and the deduction of the gamma ray events and the joining of the two-segment energy spectra are carried out by using the off-line data analysis programs written in the ROOT data analysis framework. Furthermore, an artificial neural network technique is used to accomplish the unfolding of the neutron spectra successfully. The experimental results of the second neutron angular spectra from 9cm and 18cm thick polythene slab assemblies with D-T neutron source in an energy region of 0.5 MeV to 15 MeV are obtained. The Monte Carlo calculations of the experimental models are accomplished by using the MCNP5 code with ENDF-VI data library. The experimental results are in agree ment with the calculation results within the experimental uncertainties.