A prototype of the transmission line magnet for the Low Field Very Large Hadron Collider is being designed at Fermilab. This is a single-turn warm iron superconducting magnet in a "Double-C" configuration. Iron poles form a high quality alternating-gradient 3%/cm magnet field in two 20 mm height beam gaps. Simple magnet construction and manufacturing processes and a room temperature iron yoke give a significant reduction in a magnet cost. The magnet mechanical stability was investigated for several mechanical models. A high field quality over the whole range (0.1T – 2.0T) of field variation was calculated using correcting holes and crenellations in the iron poles. The 2D and 3D magnet field analysis and optimization was carried out by POISSON, OPERA 2D, TOSCA and ANSYS codes. The results of magnet design and model tests are presented.