A magneto-resistance effect magnetic head in which the MR effects of the two MR thin films of a MR device are balanced for suppressing Barkhausen noise and assuring a stabilized output. Between a lower-layer magnetic shield core and an upper layer magnetic shield core is arranged an MR device, made up of two MR thin films such that a distance d.sub.1 between the lower-layer magnetic shield core and the MR thin film is smaller than a distance d.sub.2 between the upper-layer magnetic shield core and the MR thin film. A film thickness t.sub.1 of the MR thin film towards the lower-layer magnetic shield core is set so as to be thinner than a film thickness t.sub.2 of the MR thin film towards the upper-layer magnetic shield core. Preferably, the relation 0.5 3 holds.