The purpose of this paper is to address the avoidance of patterns of length 3 in convolved perfect matchings. We employ algebraic generating functions as a powerful tool in combinatorics in order to enumerate the avoidance of the pattern 312 in convolved perfect matchings. The generating function used by Bloom and Elizalde to asymptotically enumerate the 312-avoiding matchings, is exploited by us for proposing a new recurrence relation. We also propose three explicit formulas and one recurrence relation to enumerate the avoidance of the same pattern in convolved perfect matchings with some calculated data.