According to the problem, the equation of the hyperbola is $\frac{x^2}{4} - \frac{y^2}{3} = 1$,
thus $a^2=4$, $b^2=3$,
then $c= \sqrt{a^2+b^2}= \sqrt{7}$,
therefore, its eccentricity $e= \frac{c}{a}= \frac{\sqrt{7}}{2}$;
Hence, the answer is $\boxed{\frac{\sqrt{7}}{2}}$.
Based on the problem, the values of $a^2$ and $b^2$ can be obtained from the equation of the hyperbola, and the value of $c$ can be derived from the geometric properties of the hyperbola, which then allows for the calculation of the eccentricity using the formula for the eccentricity of a hyperbola.
This question examines the geometric properties of hyperbolas, with a key focus on being familiar with the standard form of the equation of a hyperbola.

To find the eccentricity $e$ of the hyperbola, recall the standard form of a hyperbola equation:

$$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$

where $a$ and $b$ are the lengths of the semi-major and semi-minor axes respectively, and the eccentricity $e$ is defined as:

$$e = \sqrt{1 + \frac{b^2}{a^2}}$$

However, this definition changes for a hyperbola to:

$$e = \sqrt{1 + \frac{a^2}{b^2}}$$

since $a^2$ corresponds to the term with the positive coefficient.

Given the hyperbola equation $\frac {x^{2}}{4} - \frac {y^{2}}{3} = 1$, we can identify that:

$$a^2 = 4 \quad \text{and} \quad b^2 = 3$$

Thus, the distance $c$ from the center to a focus of the hyperbola is:

$$c = \sqrt {a^2 + b^2} = \sqrt {4 + 3} = \sqrt {7}$$

Finally, the eccentricity $e$ of the hyperbola is:

$$e = \frac {c}{a} = \frac {\sqrt {7}}{2}$$

Therefore, the eccentricity of the given hyperbola is $\boxed{\frac {\sqrt {7}}{2}}$.