Yes, mold can cause asthma.

More Info: A study published in Annals Allergy Asthma Immunology found that infants that grew up in an environment where mold was visible were seven times more likely to develop asthma than those who do not.  Mold is also a know trigger for an asthma attack for those suffering from asthma.

Mold exposure during infancy as a predictor of potential asthma development. Annals Allergy Asthma Immunology

What Is a Mold Allergy?

A mold allergy occurs when a person's immune system overreacts to the inhalation of mold spores. Mold requires water and either plant or animal matter to grow, and it reproduces most quickly in dark, damp areas. Mold reproduces by forming airborne spores. Those with mold allergies can exhibit various symptoms, including coughing, irritated eyes, rash and nasal discharge. Mold can also colonize within the lungs and sinuses, though they do not cause infection. Thousands of types of mold exist, but few are available for allergy testing. Aspergillus, penicillium and cladosporium, the most common outdoor mold, are some types of mold. 

Who Is Susceptible to a Mold Allergy?

Those with a family history of asthma and allergies, regardless of the allergy, are most susceptible to a mold allergy. However, those who work in occupations which expose them to high levels of mold are also susceptible to developing a mold allergy. Occupations with high exposure to mold include farming, dairy work, baking, logging and carpentry. Because mold requires moisture to reproduce, those who live in homes with high humidity, meaning higher than 60 percent, are also susceptible to mold allergy. Homes with poor ventilation can also create optimal conditions for mold growth, especially in damp rooms such as bathrooms.