We investigate the dynamics of a Λ-type giant atom (GA) whose both transition coupled to the guided modes of a one-dimensional (1D) waveguide at two spatially separated points with the GA initially excited and the electromagnetic (EM) modes of waveguide in vacuum. The spontaneous emission properties of this GA is investigated by solving the delay-differential equation for the amplitude of the 3GA in its excited state. Signatures of non-Markovian behavior is manifested in a population trapping in the excited state of the GA in the regime where the distance d of the coupling points is smaller or comparable to the coherent length L characterizing the width of the emitted wave packet. And an exact Markovian dynamics is also found when d ≥ L via the inference by adjusting the energy spacing and the inherent time delay besides the complex phases in the atom-light coupling, matching the behavior of a small atom coupled to a waveguide.