Effects of pressure P on the magnetic moment M and the Curie temperature T C have been investigated for La(Fe x Si 1Àx ) 13 above and below the magnetic phase boundary concentration x ¼ 0:86, where the ferromagnetic-paramagnetic transition at T C changes from the first-order (x ! 0:86) to the second-order (x < 0:86). The pressure coefficient of M exhibits a sluggish variation against concentration and no anomaly was observed at x ¼ 0:86, being consistent with the Landau expansion model. On the other hand, T C for the second-order transition has a large negative pressure coefficient dT C =dP and its magnitude increases with increasing x. Above x ¼ 0:86, the magnitude of dT C =dP for the first-order transition increases with x, contrary to the theoretical expectation. It has been revealed that the spin-wave dispersion coefficient becomes smaller when the first-order transition becomes clear by changing the concentration and also applying pressure. Consequently, it is plausible that dT C =dP above x ¼ 0:86 is enhanced by the increase of instability of the ferromagnetic state.