The dependence of electrical conductivity on compression of a freestanding three-dimensional carbon nanotube (CNT) network is investigated. This macrostructure is made of mm-long and entangled CNTs, forming a random skeleton with open pores. The conductivity linearly increases with the applied compression. This behaviour is due to increase of percolating pathways—contacts among neighbouring CNTs—under loads that is highlighted by in situ scanning electron microscopy analysis. The network sustains compressions up to 75% and elastically recovers its morphology and conductivity during the release period. The repeatability coupled with the high mechanical properties makes the CNT network interesting for pressure-sensing applications.