The MAX-phase Ti$_3$AlC$_2$ has been fabricated by sintering of the preliminary cold-pressed mixtures of elemental powders of Ti, Al and C with different contents of B$_2$O$_3$ under pressure of 320 and 640 MPa, respectively. Identification and quantification of the phases have been performed by X-ray diffraction. It has been shown when we increase concentration of boron oxide up to 5% wt. in the initial Ti$_3$Al$_{1.1}$C$_2$ powder mixture cold-pressed at 320 MPa the percentage of the MAX-phase Ti$_3$AlC$_2$ in the pellets after sintering rises up to $\sim$98.5% wt. It has been found that at the high compacting pressure of 640 MPa, the fraction of the MAX-phase Ti$_3$AlC$_2$ in the sintered pellets also abruptly increases up to $\sim$98% wt. In this instance the boron oxide amount added to the initial powder mixture before pressing was low as 1% wt. Thus, it has been found that there is a clear relationship between the percentage of boron oxide in the initial powder mixture, pressing pressure and percentage of the MAX-phase after sintering, $i.e.$ the higher compacting pressure the less amount of the boron oxide should be added to the initial powder mixture to achieve high yield of MAX-phase.