The dust cloud TGU H645 P2 and embedded in it the young open cluster NGC 7129 are investigated using the results of medium-band photometry of 159 stars in the Vilnius seven-colour system down to V=18.8mag. The photometric data were used to classify about 50 per cent of the measured stars in spectral and luminosity classes. The extinction A_V_ versus distance diagram for the 20'x20' area is plotted for 155 stars with two-dimensional classification from the present and the previous catalogues. The extinction values are found in the range between 0.6 and 3.4mag. However, some red giants, located in the direction of the dense parts of the cloud, exhibit the infrared extinction equivalent up to A_V_=13mag. The distance to the cloud (and the cluster) is found to be 1.15kpc (the true distance modulus 10.30mag). For determining the age of NGC 7129, a luminosity versus temperature diagram for six cluster members of spectral classes B3-A1 was compared with the Pisa pre-main-sequence evolution tracks and the Palla birthlines. The cluster can be as old as about 3Myr, but star formation continues till now as witnessed by the presence in the cloud of many younger pre-main-sequence objects identified with photometry from 2MASS, Spitzer and WISE infrared surveys.