How to smooth matplotlib contour plot?

As others have already pointed out, you need to interpolate your data.

There are a number of different ways to do this, but for starters, consider scipy.ndimage.zoom.

As a quick exmaple:

import numpy as np
import scipy.ndimage
import matplotlib.pyplot as plt

data = np.loadtxt('data.txt')

# Resample your data grid by a factor of 3 using cubic spline interpolation.
data = scipy.ndimage.zoom(data, 3)

plt.contour(data)
plt.show()