Cross sections for (n,2n) and (n,p) reactions have been measured on tellurium isotopes at the neutron energies of 13.5−14.6 MeV using the activation technique. Data are reported for the following reactions: 120Te(n,2n)119mTe, 120Te(n,2n)119gTe, 122Te(n,2n)121mTe, 122Te(n,2n)121gTe, 124Te(n,2n)123mTe, 128Te(n,2n)127gTe, 130Te(n,2n)129mTe, 120Te(n,p)120mSb, 122Te(n,p)122m+gSb, 124Te(n,p)124m+gSb, 126Te(n,p)126m+gSb and 128Te(n,p)128m+gSb. These new data for the cross sections of tellurium isotopes have smaller uncertainties than those reported in the previous literature. The first data for the 120Te(n,p)120mSb reaction cross sections are presented. In our experiment, natural high-purity tellurium powder was used as target material and the samples were wrapped in cadmium foil during the irradiation so the influence of the (n,γ) reactions of thermal neutrons was reduced to a low level and the interfering reactions were avoided or subtracted. The HPGe detector employed in this work has better resolution than NaI(Tl). Furthermore, while gamma-ray yields were measured and then turned into cross sections using the formula in Sect. 2.2, the most recent and accurate nuclear data available were adopted. These cumulative improvements should make our results more accurate and reliable than those reported in the previous literature. Our results are useful for verifying the accuracy of nuclear models used in the calculation of cross sections and are expected to help new evaluations of the 14 MeV neutron cross sections on isotopes of tellurium.