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This study addresses Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD) under uncertainty and environmental constraints, reflecting the complexity of real-world logistics systems. Each customer requires both pickup and delivery services, neglecting time-dependent traffic conditions and demand uncertainty can lead to inefficient routing decisions. A robust mixed-integer linear programming is proposed to address the issues, which combines the fuzzy representations of demand and time-dependent travel times to increase the realism of the solution. In this research, a linear piecewise function whose slopes are greater than -1 is employed to ensure the First-In-First-Out (FIFO) property in travel time estimation. The primary objective of the proposed model is to minimize overall service time for customers, while accounting for the impact of time-sensitive traffic and environmental conditions. This approach also supports sustainability objectives by reducing carbon emissions. Given the NP-hard nature of the problem, a Variable Neighborhood Search (VNS) algorithm is utilized to efficiently solve the model. This proposed algorithm is validated through extensive computational experiments on small-, medium-, and large-scale instances. The results demonstrate that the proposed approach can significantly reduce service time and carbon emissions compared to existing methods, highlighting its effectiveness and relevance in the context of sustainable vehicle routing under uncertainty.