I switched to a new company. From my previous company , I got some stocks. I have to execute those stock within 2 months. I used Fidelity in my previous company. But If I use fidelity to sell these stocks, they will charge huge fee. What is the best way to execute these stocks and how?

Is this really stock or are they stock options? I've never heard of a company requiring that you sell shares of stock that you own outright if you leave, but it's common for companies to require that unexercised options be exercised within a couple of months of leaving. If these are options then you are stuck with Fidelity, as that's the firm your previous employer contracted with to administer options for their employees. But if in fact you truly mean stock shares you own but are held at Fidelity you can either:

a) Use Fidelity to sell them - you say their fees are "huge" but they are actually known for being quite reasonable. What do you mean by "huge?"

b) Have the stock transferred to another broker, and then sell the stock from that new account. You can set up an account at a broker such as Schwab or E-Trade and then instruct them to fund the account by transferring stock in from your Fidelity account. Of course this only makes sense if their fees are less than Fidelity's.