Checking if each char in a string is a decimal digit
In the cctype header, you have the std::isdigit(int) function. You can use this instead of your conditions that check if the character is between '0' and '9'.
You index into a std::string with an int inside the for loop. Use std::string::size_type as that is the proper type that can index into a std::string (int might be too small).
Mark the function as noexcept.
Consider passing the std::string parameter by reference if you're planning on using large number strings (~20 character numbers). This prevents unnecessary copying from dynamically allocated strings.
Check vs. the size instead of indexing into the string and checking if the current character is '\0'.
Qualify standard types with std::. Don't use using namespace std;.
There is no need to negate that first condition.
Bug: isNum("-") and isNum("+") return true. An additional check is required if the first character is '+' or '-'.
Naming is important. Your function is called isNum(), but I believe that isInt() better describes it; the function does not detect floating point numbers. Please also consider this comment by Toby Speight in regards to naming.


After changes are applied:

#include &lt;string&gt;
#include &lt;cctype&gt;

bool isinteger(std::string const&amp; n) noexcept
{
    if (std::isdigit(n[0]) || (n.size() &gt; 1 &amp;&amp; (n[0] == '-' || n[0] == '+')))
    {
        for (std::string::size_type i{ 1 }; i &lt; n.size(); ++i)
            if (!std::isdigit(n[i]))
                return false;

        return true;
    }
    return false;
}


Note 1: I've renamed the function to isinteger() to keep consistency with other similar functions such as isdigit(). I've also reordered the initial condition to take advantage of boolean short circuiting.

Note 2: As Rakete1111 points out, if your compiler hasn't caught up to C++11 yet, accessing the first character of an empty string is undefined behaviour.

The condition should be modified like so:

// check that the string is not empty, only if we're working with &lt; C++11
if ((!n.empty() &amp;&amp; std::isdigit(n[0])) || (n.size() &gt; 1 &amp;&amp; (n[0] == '-' || n[0] == '+')))
{
    // ...
}


However, if your compiler is C++11 (or later) compliant, you can safely leave it; accessing the first character of empty strings returns '\0' in that case.

See here for more information: http://en.cppreference.com/w/cpp/string/basic_string/operator_at