Yes, it is possible. There is a genetic component to height - you do get tall and short families, of course - but factors like diet play a big role too. Broadly speaking, a diet high in animal protein tends to make people grow taller. In Japan, for instance, the national diet used to contain very little meat as there was a lack of large animals, among other reasons. Nowadays people in Japan have a lot more meat and dairy products than they used to, and the average height and weight have increased. (This doesn't mean that taller people are necessarily healthier, though - a lot of animal protein may not be te best thing for you.)
The increase in Western countries has been less dramatic, but here too we are taller on average than we used to be. So although you may well stay around the same height as the rest of your family, if you've had a very different diet in childhood your height could be slightly different too (probably only slightly.)
The increase in Western countries has been less dramatic, but here too we are taller on average than we used to be. So although you may well stay around the same height as the rest of your family, if you've had a very different diet in childhood your height could be slightly different too (probably only slightly.)