An existing Nb3Sn laboratory magnet generating a magnetic field of 12 T is intended to be upgraded to 16 T by means of the use of a high temperature superconductor (HTS) insert coil. An outline design of the HTS insert coil is presented. In the design, the aspects of the maximum achievable operation current, the required copper cross-section to ensure a hot spot temperature below 200 K and the resulting forces and stresses have been considered. The length of the insert coil has been selected in such a way that the field uniformity will be better than 1% within a sphere of 3 cm diameter. The protection of the whole magnet system (LTS & HTS insert) is briefly described. (C) 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Guest Editors.