We present the results of NTT/VLT UBV imaging of a 260 square arcmin region containing the Galactic Luminous Blue Variable WRA751, in search for its birth-cluster, i.e. a cluster of young and massive stars spatially and physically associated with it. On the basis of the classical reddening-free parameter Q, we have identified a sample of 24 early-type stars with colours typical of spectral types earlier than B3. Interestingly, these stars are clustered within a radius of 1 arcmin from WRA751, corresponding to about 1% of the imaged field. These stars tightly distribute around (B-V) = 1.67, which in turn defines a mean extinction A(V) = 6.1 mag. The 5 brighter (V > 16.2) and bluer (Q < -0.9) stars of the sample have been subsequently observed with FORS1 and classified as 3 late O- and 2 early B- stars. The absence of stars earlier than O8 indicates an age of the cluster older than 4 Myr, although it could be due to an incomplete sampling of the upper end of the main sequence. Nevertheless, the detection of OB stars of class I certainly indicates an age of a few million years. At an assumed distance of 6 kpc, we estimate a cluster radius of 3.4 pc and a total mass of 2200 solar masses. Our discovery is only the second known instance of a Galactic Luminous Blue Variable associated with its birth-cluster.