Electronic and magnetic proper tis of the rare-earth transition metal compound, $LaCo_{13}$, are investigated by performing self-consistent local density functional LMTO (linearized muffin-tin orbital) band structure calculations for both paramagnetic and ferromagnetic phases of $LaCo_{13}$. The calculated magnetic moments for the two types of Co atoms, Co I and Co II, are 1.34 and $1.65{mu}_{B}$, respectively. The average magnetic moment of Co atoms in the ferromagnetic phase of $LaCo_{13}$ is estimated to be $1.60{mu}_{B}$, which is in fairly good agreement with the experimental values, $1.56~1.68{mu}_{B}$.