The pressure dependence of the effective mass m* of the negative ion in He I1 has been investigated for the first time. On the assumption of a free-particle-like ionic dispersion relation, the values of m* deduced from the measurements range from 108m4 at 11 bar to 77m4 at 25 bar, where m4 is the 4He atomic mass. There are indications in the raw data, however, that there may be a small quartic term in the dispersion relation. If the data are re-analysed on the assumption that such an extra term does exist, the derived values of m' are reduced by about 8%, which then brings them into excellent agreement with the predictions of the bubble model of the negative ion.