Dosimetric measurements of fast neutrons at a level lower than 10 mrem from an Am-Be source have been made by using CR-39 plastic sheets. After being etched in 6.8N NaOH for 18 to 20 h, the CR-39 sheets were scanned under an optical microscope and counted, with the requirement that etch pits have sharp tips. The background pits due to alpha-particles at the surface of sheets are eliminated by this criterion. The density of etch pits as a function of rem-dose shows excellent linearity over the range of 1 to 10 mrem. The sensitivity is 13.4 etch pits/cm mrem.