In the age of Big Data, enabling task scheduling while protecting users' privacy is critical for various decentralized applications in blockchain-based smart contract platforms. Such a privacy-preserving task scheduler requires the task input data to be secretly maintained until a prescribed task execution time and be automatically recorded into the blockchain to enabling the execution of the task at the execution time, even if the user goes offline. While straight-forward centralized approaches provide a basic solution to the problem, unfortunately they are limited to a single point of trust and involve a single point of control. This paper presents decentralized techniques for supporting privacy-preserving task scheduling using smart contracts in Ethereum blockchain networks. We design a privacy-preserving task scheduling protocol that is managed by a manager smart contract. The protocol requires a user to schedule a task by deploying a proxy smart contract maintaining the non-sensitive information of the task while creating decentralized secret trust and selecting trustees from the network to maintain the sensitive information of the task. With security techniques including secret sharing and layered encryption as well as security deposit paid by trustees as economic deterrence, the protocol can protect the sensitive information against possible attacks including some trustees destroying the sensitive information (drop attack) or secretly releasing the sensitive information before the execution time (release-ahead attack). We demonstrate the attack-resilience of the proposed protocol through rigorous analysis.Our implementation and experimental evaluation on the Ethereum official test network demonstrate the low monetary cost and the low time overhead associated with the proposed approach.