I am planning to trade stocks in the stock market but I can't open an account in a broker because I don't have a passport or driver's license. So I plan on letting my older brother make an account on a broker where in I will deposit my own funds and then trade in the stock market. May I know if this is illegal?
The rules that govern this are called Know Your Customers rules:
Depending on your location it might not be strictly illegal for you to do it, but be certain that your (well, your brother's) financial institution will have problems with it.
Most brokerages have a process to enact a "power of attorney" (POA) relationship, to allow a family member (siblings are specifically identified at this US FINRA page as a typical case) to make trades on behalf of the account owner.
So to the isolated title question: yes, it is legal and possible for a sibling to have a power of attorney granted by the brother to trade in the brother's owned brokerage account.
That said, I can't tell if the brokerage would need the identification you don't have to enable this; and further, in the details of the question, the intended ownership of the account becomes cloudy, and I am not sure if a POA would insulate the sequence where you gift your brother money, invest the money, and take the money later on. Also there is the risk to you that at any point, the brother retracts the POA, and remains the owner of the funds in the account.