Large language models (LLMs) with diverse capabilities are increasingly being deployed in local environments, presenting significant security and controllability challenges. These locally deployed LLMs operate outside the direct control of developers, rendering them more susceptible to abuse. Existing mitigation techniques mainly designed for cloud-based LLM services are frequently circumvented or ineffective in deployer-controlled environments. We propose SECNEURON, the first framework that seamlessly embeds classic access control within the intrinsic capabilities of LLMs, achieving reliable, cost-effective, flexible, and certified abuse control for local deployed LLMs. SECNEURON employs neuron-level encryption and selective decryption to dynamically control the task-specific capabilities of LLMs, limiting unauthorized task abuse without compromising others. We first design a task-specific neuron extraction mechanism to decouple logically related neurons and construct a layered policy tree for handling coupled neurons. We then introduce a flexible and efficient hybrid encryption framework for millions of neurons in LLMs. Finally, we developed a distribution-based decrypted neuron detection mechanism on ciphertext to ensure the effectiveness of partially decrypted LLMs. We proved that SECNEURON satisfies IND-CPA Security and Collusion Resistance Security under the Task Controllability Principle. Experiments on various task settings show that SECNEURON limits unauthorized task accuracy to below 25% while keeping authorized accuracy loss with 2%. Using an unauthorized Code task example, the accuracy of abuse-related malicious code generation was reduced from 59% to 15%. SECNEURON also mitigates unauthorized data leakage, reducing PII extraction rates to below 5% and membership inference to random guesses.