Vegetal proteins are of high interest for their many positive aspects, but their ‘beany’ off-flavor is still limiting the consumer’s acceptance. The aim of this work was to investigate the conservation of pea protein isolate (PPI) during time and especially the evolution of their organoleptic quality under two storage conditions. The evolution of the volatile compounds, the odor and the color of a PPI has been investigated during one year of storage. PPI was exposed to two treatments mimicking a lack of control of storage conditions: treatment A with light exposition at ambient temperature (A—Light 20 °C) and treatment B in the dark but with a higher temperature (B—Dark 30 °C). For each sampling time (0, 3, 6, 9, 12 months), the volatile compounds were determined using HS-SPME-GC-MS, the odor using direct sniffing, and the color using the measurement of L*, a*, b* parameters. Treatment A was the most deteriorating and led to a strong increase in the total volatile compounds amount, an odor deterioration, and a color change. Furthermore, a tentative correlation between instrumental data on volatile compounds and the perceived odor was proposed. By the representation of volatile compounds sorted by their sensory descriptor, it could be possible to predict an odor change with analytical data.