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In this paper, we calculate the 2-local unstable homotopy groups ofindecomposable $\mathbf{A}_3^2$-complexes. The main technique used is analysingthe homotopy property of $J(X,A)$, defined by B. Gray for a CW-pair $(X,A)$,which is homotopy equivalent to the homotopy fibre of the pinch map $X\cupCA\rightarrow \Sigma A$.

2-local unstable homotopy groups of indecomposable $\mathbf{A}_3^2$ -complexes