Linear thermal expansion coefficient (LTEC) of single crystal k-(D4-BEDT-TTF)2Cu[N(CN)2]Br was studied across the crystal layers in the temperature range 2-290 K using the method of precise capacitive dilatometry. Below Tc = 11,6 K the LTEC of the sample had a small negative value, which is apparently due to the transition from the paramagnetic metal in the superconducting state. There was a bend of temperature dependence of the LTEC, which shows broad peak around 40 K and can be attributed to the elastic lattice anomaly around the end-point of Mott boundary. A sharp jump in the LTEC values and hysteresis was observed in the area of Tg ~ 75-77 K, what is likely explained by the transition in a glass-like state. The isotope effect in the thermal expansion is discusses, which manifested itself in a shift of the phase transitions in comparison with fully deuterated BEDT-TTF sample.