This work analyzes innovation growth in the economy in condition of increase of natural resources extraction in a model framework. The main stylized fact for the model is that the economic growth in Russia in two last decades was not well balanced and a sufficient part of it was due to high prices of natural exhaustible resources (oil and gas). On the other side, there were also successful attempts to induce the growth based on the competency development. An endogenous growth model has been developed. It reflects both the growth of the resource extraction and the growth, connected with the increase in technological level of the economy. This model may be useful for a number of developing countries, which budget is in direct dependence on oil and gas exports. The model is discrete and multi-periodic one. © 2016, Education and Upbringing Publishing. All rights reserved.