The paramagnetic Y3-0.02-x Er0.02Yb x Al5O12 (x = 0.02, 0.06, 0.10, 0.12, 0.18, 0.20) nanocrystals (NCs) were synthesized by the microwave-induced solution combustion method. The XRD, TEM and SEM techniques were applied to determine the NCs' structures and sizes. The XRD patterns confirmed that the NCs have for the most part a regular structure of the Y3Al5O12 (YAG) phase. The changes of the distance between donor Yb3+ (sensitizer) and acceptor Er3+ (activator) were realized by changing the donor's concentration with a constant amount of acceptor. Under 980 nm excitation, at room temperature, the NCs exhibited strong red emission near 660 and 675 nm, and green upconversion emission at 550 nm, corresponding to the intra 4f transitions of Er3+ (4F9/2, 2H11/2, 4S3/2) → Er3+ (4I15/2). The strongest emission was observed in a sample containing 18% Yb3+ ions. The red and green emission intensities are respectively about 5 and 12 times higher as compared to NCs doped with 2% of Yb3+. In order to prove that the main factor responsible for the increase of the upconversion luminescence efficiency is reduction of the distance between Yb3+ and Er3+, we examined, for the first time the influence of hydrostatic pressure on luminescence and luminescence decay time of the radiative transitions inside donor ion. The decrease of both luminescence intensity and luminescence decay times, with increasing hydrostatic pressure was observed. After applying hydrostatic pressure to samples with e.g. 2% and 6% Yb3+, the distance between the donor and acceptor decreases. However, for higher concentrations of the donor, this distance is smaller, and this leads to the effective energy transfer to Er3+ ions. With increasing pressure, the maximum intensity of near infrared emission is observed at 1029, 1038 and 1047 nm, what corresponds to 2F5/2 → 2F7/2 transition of Yb3+.